Model Analysis
Nikhil Gupta
2019-02-09 15:02:19
sessionInfo()## R version 3.5.1 (2018-07-02)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17134)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252
## [2] LC_CTYPE=English_United States.1252
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## loaded via a namespace (and not attached):
## [1] compiler_3.5.1 magrittr_1.5 tools_3.5.1 htmltools_0.3.6
## [5] yaml_2.2.0 Rcpp_1.0.0 stringi_1.2.4 rmarkdown_1.11
## [9] knitr_1.20 stringr_1.3.1 digest_0.6.18 evaluate_0.12User Inputs
output.var = params$output.var
transform.abs = params$transform.abs
log.pred = params$log.pred
eda = params$eda
algo.forward = params$algo.forward
algo.backward = params$algo.backward
algo.stepwise = params$algo.stepwise
algo.LASSO = params$algo.LASSO
algo.LARS = params$algo.LARS
message("Parameters used for training/prediction: ")## Parameters used for training/prediction:str(params)## List of 9
## $ output.var : chr "y3"
## $ transform.abs: logi FALSE
## $ log.pred : logi FALSE
## $ eda : logi FALSE
## $ algo.forward : logi TRUE
## $ algo.backward: logi FALSE
## $ algo.stepwise: logi FALSE
## $ algo.LASSO : logi FALSE
## $ algo.LARS : logi FALSE# Setup Labels
# alt.scale.label.name = Alternate Scale variable name
# - if predicting on log, then alt.scale is normal scale
# - if predicting on normal scale, then alt.scale is log scale
if (log.pred == TRUE){
label.names = paste('log.',output.var,sep="")
alt.scale.label.name = output.var
}
if (log.pred == FALSE){
label.names = output.var
alt.scale.label.name = paste('log.',output.var,sep="")
}Prepare Data
Read and Clean Features
features = read.csv("../../Data/features.csv")
#str(features) Checking correlations to evaluate removal of redundant features
corr.matrix = round(cor(features[sapply(features, is.numeric)]),2)
# filter out only highly correlated variables
threshold = 0.6
corr.matrix.tmp = corr.matrix
diag(corr.matrix.tmp) = 0
high.corr = apply(abs(corr.matrix.tmp) >= threshold, 1, any)
high.corr.matrix = corr.matrix.tmp[high.corr, high.corr]
DT::datatable(corr.matrix)DT::datatable(high.corr.matrix)Feature Names
feature.names = colnames(features)
drops <- c('JobName')
feature.names = feature.names[!(feature.names %in% drops)]
#str(feature.names)Read and Clean Labels
labels = read.csv("../../Data/labels.csv")
#str(labels)
labels = labels[,c("JobName", output.var)]
summary(labels)## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.21
## Job_00003: 1 Median :123.99
## Job_00004: 1 Mean :125.36
## Job_00005: 1 3rd Qu.:131.06
## Job_00006: 1 Max. :193.73
## (Other) :9994 NA's :2497Merge Datasets
data <- merge(features, labels, by = 'JobName')
drops <- c('JobName')
data = data[,(!colnames(data) %in% drops)]
#str(data)Transformations
if (transform.abs == TRUE){
data[,label.names] = 10^(data[,label.names]/20)
data = filter(data, y3 < 1E7)
}
#str(data)
if (log.pred == TRUE){
data[label.names] = log(data[alt.scale.label.name],10)
drops = c(alt.scale.label.name)
data = data[!(names(data) %in% drops)]
}
#str(data)Remove NA Cases
data = data[complete.cases(data),]Exploratory Data Analysis
Check correlation of Label with Featires
if (eda == TRUE){
corr.to.label =round(cor(dplyr::select(data,-one_of(label.names)),dplyr::select_at(data,label.names)),4)
DT::datatable(corr.to.label)
}Multicollinearity - VIF
if (eda == TRUE){
vifDF = usdm::vif(select_at(data,feature.names)) %>% arrange(desc(VIF))
head(vifDF,10)
}Scatterplots
panel.hist <- function(x, ...)
{
usr <- par("usr"); on.exit(par(usr))
par(usr = c(usr[1:2], 0, 1.5) )
h <- hist(x, plot = FALSE)
breaks <- h$breaks; nB <- length(breaks)
y <- h$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col = "cyan", ...)
}if (eda == TRUE){
histogram(data[ ,label.names])
#hist(data[complete.cases(data),alt.scale.label.name])
}# https://stackoverflow.com/questions/24648729/plot-one-numeric-variable-against-n-numeric-variables-in-n-plots
ind.pairs.plot <- function(data, xvars=NULL, yvar)
{
df <- data
if (is.null(xvars)) {
xvars = names(data[which(names(data)!=yvar)])
}
#choose a format to display charts
ncharts <- length(xvars)
for(i in 1:ncharts){
plot(df[,xvars[i]],df[,yvar], xlab = xvars[i], ylab = yvar)
}
}
if (eda == TRUE){
ind.pairs.plot(data, feature.names, label.names)
}
#
# pl <- ggplot(data, aes(x=x18, y = y3))
# pl2 <- pl + geom_point(aes(alpha = 0.1)) # default color gradient based on 'hp'
# print(pl2)Feature Engineering
if(eda ==FALSE){
# x18 may need transformations
plot(data[,'x18'], data[,label.names], main = "Original Scatter Plot vs. x18", ylab = label.names, xlab = 'x18')
plot(sqrt(data[,'x18']), data[,label.names], main = "Original Scatter Plot vs. sqrt(x18)", ylab = label.names, xlab = 'sqrt(x18)')
# transforming x18
data$sqrt.x18 = sqrt(data$x18)
data = dplyr::select(data,-one_of('x18'))
# what about x7, x9?
# x11 looks like data is at discrete points after a while. Will this be a problem?
}
Modeling
Train Test Split
data = data[sample(nrow(data)),] # randomly shuffle data
split = sample.split(data[,label.names], SplitRatio = 0.8)
data.train = subset(data, split == TRUE)
data.test = subset(data, split == FALSE)Common Functions
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
plot(predict(model,train),r.student,
ylab="Student Residuals", xlab="Predicted Values",
main="Student Residual Plot")
abline(0, 0)
plot(predict(model, train),r.standard,
ylab="Standard Residuals", xlab="Predicted Values",
main="Standard Residual Plot")
abline(0, 0)
abline(2, 0)
abline(-2, 0)
# Histogram
hist(r.student, freq=FALSE, main="Distribution of Studentized Residuals",
xlab="Studentized Residuals", ylab="Density", ylim=c(0,0.5))
# Create range of x-values for normal curve
xfit <- seq(min(r.student)-1, max(r.student)+1, length=40)
# Generate values from the normal distribution at the specified values
yfit <- (dnorm(xfit))
# Add the normal curve
lines(xfit, yfit, ylim=c(0,0.5))
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
plot(lev, ylab = 'Leverage - check')
# Cook's Distance
cd = cooks.distance(model)
plot(cd,ylab="Cooks distances")
abline(4/nrow(train),0)
abline(1,0)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
test.model = function(model, test, type = 'No Model Name Specified', level = 0.95){
pred = predict(model, newdata=test, interval="confidence", level = level)
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(type, " Test MSE: ", test.mse, sep=""))
plot(test[,label.names],pred[,1],xlab = "Actual", ylab = "Predicted")
}Setup Formulae
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)## y3 ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 +
## x12 + x13 + x14 + x15 + x16 + x17 + x19 + x20 + x21 + x22 +
## x23 + stat1 + stat2 + stat3 + stat4 + stat5 + stat6 + stat7 +
## stat8 + stat9 + stat10 + stat11 + stat12 + stat13 + stat14 +
## stat15 + stat16 + stat17 + stat18 + stat19 + stat20 + stat21 +
## stat22 + stat23 + stat24 + stat25 + stat26 + stat27 + stat28 +
## stat29 + stat30 + stat31 + stat32 + stat33 + stat34 + stat35 +
## stat36 + stat37 + stat38 + stat39 + stat40 + stat41 + stat42 +
## stat43 + stat44 + stat45 + stat46 + stat47 + stat48 + stat49 +
## stat50 + stat51 + stat52 + stat53 + stat54 + stat55 + stat56 +
## stat57 + stat58 + stat59 + stat60 + stat61 + stat62 + stat63 +
## stat64 + stat65 + stat66 + stat67 + stat68 + stat69 + stat70 +
## stat71 + stat72 + stat73 + stat74 + stat75 + stat76 + stat77 +
## stat78 + stat79 + stat80 + stat81 + stat82 + stat83 + stat84 +
## stat85 + stat86 + stat87 + stat88 + stat89 + stat90 + stat91 +
## stat92 + stat93 + stat94 + stat95 + stat96 + stat97 + stat98 +
## stat99 + stat100 + stat101 + stat102 + stat103 + stat104 +
## stat105 + stat106 + stat107 + stat108 + stat109 + stat110 +
## stat111 + stat112 + stat113 + stat114 + stat115 + stat116 +
## stat117 + stat118 + stat119 + stat120 + stat121 + stat122 +
## stat123 + stat124 + stat125 + stat126 + stat127 + stat128 +
## stat129 + stat130 + stat131 + stat132 + stat133 + stat134 +
## stat135 + stat136 + stat137 + stat138 + stat139 + stat140 +
## stat141 + stat142 + stat143 + stat144 + stat145 + stat146 +
## stat147 + stat148 + stat149 + stat150 + stat151 + stat152 +
## stat153 + stat154 + stat155 + stat156 + stat157 + stat158 +
## stat159 + stat160 + stat161 + stat162 + stat163 + stat164 +
## stat165 + stat166 + stat167 + stat168 + stat169 + stat170 +
## stat171 + stat172 + stat173 + stat174 + stat175 + stat176 +
## stat177 + stat178 + stat179 + stat180 + stat181 + stat182 +
## stat183 + stat184 + stat185 + stat186 + stat187 + stat188 +
## stat189 + stat190 + stat191 + stat192 + stat193 + stat194 +
## stat195 + stat196 + stat197 + stat198 + stat199 + stat200 +
## stat201 + stat202 + stat203 + stat204 + stat205 + stat206 +
## stat207 + stat208 + stat209 + stat210 + stat211 + stat212 +
## stat213 + stat214 + stat215 + stat216 + stat217 + sqrt.x18print(grand.mean.formula)## y3 ~ 1# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]Full & Grand Means Model
model.full = lm(formula , data.train)
summary(model.full)##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.046 -6.111 -1.718 4.454 67.838
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.840e+01 2.763e+00 31.993 < 2e-16 ***
## x1 -7.972e-02 1.905e-01 -0.418 0.67560
## x2 8.835e-02 1.210e-01 0.730 0.46539
## x3 2.257e-02 3.336e-02 0.676 0.49882
## x4 -1.359e-02 2.623e-03 -5.182 2.27e-07 ***
## x5 8.916e-02 8.571e-02 1.040 0.29824
## x6 2.863e-02 1.732e-01 0.165 0.86872
## x7 3.175e+00 1.857e-01 17.097 < 2e-16 ***
## x8 1.320e-01 4.308e-02 3.064 0.00219 **
## x9 9.523e-01 9.663e-02 9.855 < 2e-16 ***
## x10 3.100e-01 8.954e-02 3.462 0.00054 ***
## x11 5.331e+07 2.142e+07 2.489 0.01285 *
## x12 -8.422e-02 5.447e-02 -1.546 0.12211
## x13 2.430e-02 2.192e-02 1.109 0.26768
## x14 -1.387e-01 9.421e-02 -1.472 0.14102
## x15 1.683e-03 8.964e-02 0.019 0.98502
## x16 2.951e-01 6.240e-02 4.730 2.30e-06 ***
## x17 3.854e-01 9.463e-02 4.073 4.71e-05 ***
## x19 5.131e-02 4.841e-02 1.060 0.28921
## x20 2.337e-01 3.346e-01 0.698 0.48491
## x21 3.388e-02 1.226e-02 2.764 0.00572 **
## x22 -8.311e-02 1.004e-01 -0.827 0.40802
## x23 6.700e-02 9.550e-02 0.702 0.48297
## stat1 2.195e-02 7.198e-02 0.305 0.76046
## stat2 -4.273e-02 7.179e-02 -0.595 0.55176
## stat3 1.098e-01 7.209e-02 1.524 0.12768
## stat4 -1.610e-01 7.256e-02 -2.219 0.02654 *
## stat5 -2.961e-02 7.200e-02 -0.411 0.68093
## stat6 -4.123e-02 7.261e-02 -0.568 0.57022
## stat7 -7.323e-02 7.225e-02 -1.013 0.31088
## stat8 -2.258e-02 7.208e-02 -0.313 0.75404
## stat9 -3.576e-02 7.227e-02 -0.495 0.62078
## stat10 -1.027e-01 7.253e-02 -1.416 0.15679
## stat11 -2.215e-03 7.257e-02 -0.031 0.97565
## stat12 1.063e-02 7.194e-02 0.148 0.88253
## stat13 -1.438e-01 7.188e-02 -2.001 0.04545 *
## stat14 -2.301e-01 7.152e-02 -3.217 0.00130 **
## stat15 -4.358e-02 7.158e-02 -0.609 0.54265
## stat16 3.134e-02 7.188e-02 0.436 0.66286
## stat17 -1.838e-02 7.142e-02 -0.257 0.79694
## stat18 -5.114e-02 7.180e-02 -0.712 0.47632
## stat19 1.311e-01 7.208e-02 1.819 0.06894 .
## stat20 -7.530e-02 7.220e-02 -1.043 0.29698
## stat21 1.861e-03 7.212e-02 0.026 0.97942
## stat22 -1.102e-01 7.232e-02 -1.524 0.12750
## stat23 1.334e-01 7.131e-02 1.870 0.06151 .
## stat24 -8.660e-02 7.199e-02 -1.203 0.22906
## stat25 -1.177e-01 7.198e-02 -1.635 0.10219
## stat26 -1.638e-01 7.237e-02 -2.264 0.02364 *
## stat27 3.443e-02 7.206e-02 0.478 0.63281
## stat28 -2.020e-02 7.180e-02 -0.281 0.77845
## stat29 1.034e-01 7.217e-02 1.433 0.15190
## stat30 4.438e-02 7.256e-02 0.612 0.54080
## stat31 -5.152e-02 7.289e-02 -0.707 0.47976
## stat32 1.896e-02 7.281e-02 0.260 0.79454
## stat33 -1.151e-01 7.182e-02 -1.603 0.10898
## stat34 3.819e-02 7.220e-02 0.529 0.59693
## stat35 -1.254e-01 7.240e-02 -1.733 0.08322 .
## stat36 -7.906e-03 7.185e-02 -0.110 0.91239
## stat37 -1.549e-01 7.274e-02 -2.129 0.03327 *
## stat38 1.101e-01 7.229e-02 1.523 0.12789
## stat39 -7.236e-02 7.176e-02 -1.008 0.31334
## stat40 1.511e-02 7.221e-02 0.209 0.83424
## stat41 -1.708e-01 7.160e-02 -2.385 0.01710 *
## stat42 -6.158e-02 7.198e-02 -0.855 0.39235
## stat43 -1.446e-01 7.234e-02 -1.999 0.04571 *
## stat44 4.068e-02 7.207e-02 0.564 0.57250
## stat45 -1.289e-01 7.178e-02 -1.796 0.07247 .
## stat46 1.531e-01 7.241e-02 2.114 0.03458 *
## stat47 3.456e-02 7.250e-02 0.477 0.63362
## stat48 1.412e-01 7.276e-02 1.941 0.05227 .
## stat49 7.022e-02 7.171e-02 0.979 0.32750
## stat50 7.797e-02 7.149e-02 1.091 0.27548
## stat51 9.101e-02 7.223e-02 1.260 0.20773
## stat52 4.669e-03 7.225e-02 0.065 0.94848
## stat53 -5.958e-02 7.241e-02 -0.823 0.41068
## stat54 -1.880e-01 7.262e-02 -2.589 0.00965 **
## stat55 6.773e-02 7.139e-02 0.949 0.34279
## stat56 -9.979e-02 7.256e-02 -1.375 0.16911
## stat57 5.973e-02 7.147e-02 0.836 0.40331
## stat58 5.918e-03 7.115e-02 0.083 0.93372
## stat59 1.007e-02 7.180e-02 0.140 0.88846
## stat60 1.235e-01 7.222e-02 1.710 0.08732 .
## stat61 -6.775e-02 7.232e-02 -0.937 0.34889
## stat62 -6.722e-02 7.225e-02 -0.930 0.35220
## stat63 5.340e-02 7.221e-02 0.740 0.45960
## stat64 -1.954e-02 7.153e-02 -0.273 0.78467
## stat65 -8.478e-02 7.256e-02 -1.168 0.24266
## stat66 5.086e-02 7.283e-02 0.698 0.48496
## stat67 4.404e-02 7.229e-02 0.609 0.54242
## stat68 -2.555e-02 7.232e-02 -0.353 0.72385
## stat69 -2.561e-02 7.193e-02 -0.356 0.72179
## stat70 1.336e-01 7.156e-02 1.867 0.06191 .
## stat71 3.658e-02 7.185e-02 0.509 0.61070
## stat72 5.099e-02 7.250e-02 0.703 0.48193
## stat73 8.757e-02 7.234e-02 1.211 0.22613
## stat74 -1.731e-02 7.234e-02 -0.239 0.81089
## stat75 -4.791e-02 7.240e-02 -0.662 0.50820
## stat76 2.352e-02 7.248e-02 0.324 0.74561
## stat77 -3.447e-02 7.233e-02 -0.477 0.63370
## stat78 -1.496e-02 7.215e-02 -0.207 0.83580
## stat79 -1.016e-02 7.228e-02 -0.141 0.88826
## stat80 4.653e-02 7.276e-02 0.640 0.52250
## stat81 3.971e-02 7.226e-02 0.550 0.58268
## stat82 2.988e-02 7.188e-02 0.416 0.67766
## stat83 -1.458e-02 7.188e-02 -0.203 0.83932
## stat84 2.757e-02 7.226e-02 0.382 0.70280
## stat85 3.421e-02 7.196e-02 0.475 0.63457
## stat86 -4.923e-03 7.198e-02 -0.068 0.94547
## stat87 -1.179e-01 7.273e-02 -1.621 0.10500
## stat88 -4.159e-02 7.152e-02 -0.581 0.56096
## stat89 -9.905e-02 7.166e-02 -1.382 0.16696
## stat90 -4.005e-02 7.212e-02 -0.555 0.57867
## stat91 -8.703e-02 7.166e-02 -1.215 0.22460
## stat92 -1.265e-01 7.226e-02 -1.751 0.08006 .
## stat93 -7.038e-02 7.340e-02 -0.959 0.33764
## stat94 -1.341e-01 7.229e-02 -1.854 0.06372 .
## stat95 6.040e-04 7.225e-02 0.008 0.99333
## stat96 -2.990e-02 7.189e-02 -0.416 0.67746
## stat97 -8.150e-03 7.167e-02 -0.114 0.90947
## stat98 1.007e+00 7.081e-02 14.220 < 2e-16 ***
## stat99 8.709e-02 7.231e-02 1.204 0.22849
## stat100 1.590e-01 7.224e-02 2.200 0.02781 *
## stat101 -7.136e-03 7.277e-02 -0.098 0.92188
## stat102 -6.611e-02 7.263e-02 -0.910 0.36276
## stat103 -6.653e-02 7.272e-02 -0.915 0.36030
## stat104 -7.868e-02 7.179e-02 -1.096 0.27317
## stat105 6.167e-02 7.140e-02 0.864 0.38781
## stat106 5.664e-04 7.171e-02 0.008 0.99370
## stat107 1.642e-02 7.215e-02 0.228 0.81999
## stat108 -6.261e-02 7.185e-02 -0.871 0.38358
## stat109 1.294e-02 7.186e-02 0.180 0.85712
## stat110 -9.497e-01 7.190e-02 -13.207 < 2e-16 ***
## stat111 3.395e-02 7.240e-02 0.469 0.63913
## stat112 5.217e-03 7.247e-02 0.072 0.94261
## stat113 -5.131e-02 7.261e-02 -0.707 0.47978
## stat114 4.506e-02 7.175e-02 0.628 0.53008
## stat115 8.659e-02 7.164e-02 1.209 0.22682
## stat116 8.653e-02 7.237e-02 1.196 0.23188
## stat117 5.161e-03 7.255e-02 0.071 0.94329
## stat118 -5.636e-02 7.185e-02 -0.784 0.43282
## stat119 2.451e-02 7.228e-02 0.339 0.73457
## stat120 5.274e-03 7.120e-02 0.074 0.94095
## stat121 4.592e-03 7.215e-02 0.064 0.94925
## stat122 1.372e-02 7.159e-02 0.192 0.84800
## stat123 -8.512e-03 7.289e-02 -0.117 0.90704
## stat124 -2.525e-02 7.222e-02 -0.350 0.72666
## stat125 1.632e-02 7.240e-02 0.225 0.82170
## stat126 4.050e-02 7.187e-02 0.563 0.57312
## stat127 -5.069e-02 7.182e-02 -0.706 0.48040
## stat128 -4.375e-02 7.211e-02 -0.607 0.54406
## stat129 -1.798e-02 7.178e-02 -0.251 0.80217
## stat130 4.264e-02 7.236e-02 0.589 0.55576
## stat131 2.524e-02 7.205e-02 0.350 0.72612
## stat132 -1.388e-02 7.220e-02 -0.192 0.84759
## stat133 -1.666e-02 7.232e-02 -0.230 0.81784
## stat134 -8.046e-02 7.208e-02 -1.116 0.26433
## stat135 -2.221e-02 7.221e-02 -0.308 0.75839
## stat136 1.236e-02 7.241e-02 0.171 0.86442
## stat137 2.432e-02 7.143e-02 0.340 0.73351
## stat138 -3.383e-02 7.207e-02 -0.469 0.63881
## stat139 2.366e-02 7.252e-02 0.326 0.74419
## stat140 -4.409e-02 7.209e-02 -0.612 0.54080
## stat141 1.077e-01 7.190e-02 1.498 0.13409
## stat142 -1.226e-02 7.270e-02 -0.169 0.86614
## stat143 9.931e-02 7.259e-02 1.368 0.17131
## stat144 1.018e-01 7.190e-02 1.416 0.15676
## stat145 3.049e-02 7.323e-02 0.416 0.67720
## stat146 -1.102e-01 7.279e-02 -1.514 0.13007
## stat147 -9.501e-02 7.270e-02 -1.307 0.19133
## stat148 -4.690e-02 7.143e-02 -0.657 0.51149
## stat149 -1.108e-01 7.274e-02 -1.524 0.12764
## stat150 -1.599e-02 7.276e-02 -0.220 0.82609
## stat151 -1.419e-01 7.277e-02 -1.950 0.05118 .
## stat152 -4.331e-02 7.190e-02 -0.602 0.54696
## stat153 4.545e-02 7.345e-02 0.619 0.53610
## stat154 -3.266e-02 7.252e-02 -0.450 0.65249
## stat155 -1.428e-03 7.228e-02 -0.020 0.98424
## stat156 1.147e-01 7.237e-02 1.586 0.11288
## stat157 2.687e-02 7.171e-02 0.375 0.70789
## stat158 -1.108e-01 7.314e-02 -1.515 0.12990
## stat159 1.418e-02 7.202e-02 0.197 0.84396
## stat160 1.427e-02 7.265e-02 0.196 0.84426
## stat161 1.083e-01 7.244e-02 1.495 0.13493
## stat162 -2.300e-02 7.169e-02 -0.321 0.74839
## stat163 1.215e-02 7.283e-02 0.167 0.86750
## stat164 8.625e-02 7.243e-02 1.191 0.23383
## stat165 1.926e-03 7.231e-02 0.027 0.97875
## stat166 -6.537e-02 7.149e-02 -0.914 0.36054
## stat167 -7.187e-02 7.178e-02 -1.001 0.31675
## stat168 -2.348e-03 7.217e-02 -0.033 0.97404
## stat169 -3.259e-02 7.206e-02 -0.452 0.65109
## stat170 -7.519e-02 7.202e-02 -1.044 0.29650
## stat171 2.792e-02 7.295e-02 0.383 0.70191
## stat172 1.292e-01 7.208e-02 1.792 0.07312 .
## stat173 -5.825e-02 7.264e-02 -0.802 0.42267
## stat174 -1.380e-02 7.255e-02 -0.190 0.84910
## stat175 -1.070e-01 7.228e-02 -1.480 0.13883
## stat176 5.254e-02 7.240e-02 0.726 0.46810
## stat177 4.772e-02 7.228e-02 0.660 0.50916
## stat178 -5.903e-02 7.296e-02 -0.809 0.41849
## stat179 2.146e-02 7.172e-02 0.299 0.76476
## stat180 4.792e-03 7.163e-02 0.067 0.94667
## stat181 -2.728e-04 7.248e-02 -0.004 0.99700
## stat182 -4.012e-02 7.249e-02 -0.553 0.57995
## stat183 8.387e-02 7.192e-02 1.166 0.24360
## stat184 -6.556e-04 7.267e-02 -0.009 0.99280
## stat185 -5.383e-02 7.118e-02 -0.756 0.44951
## stat186 -8.523e-02 7.271e-02 -1.172 0.24119
## stat187 -1.719e-01 7.204e-02 -2.386 0.01705 *
## stat188 2.188e-02 7.201e-02 0.304 0.76126
## stat189 -7.641e-03 7.225e-02 -0.106 0.91577
## stat190 3.140e-02 7.200e-02 0.436 0.66276
## stat191 -5.538e-02 7.225e-02 -0.766 0.44342
## stat192 -2.538e-02 7.263e-02 -0.350 0.72672
## stat193 -2.148e-02 7.277e-02 -0.295 0.76781
## stat194 -3.584e-02 7.209e-02 -0.497 0.61906
## stat195 7.298e-02 7.212e-02 1.012 0.31165
## stat196 -6.267e-02 7.298e-02 -0.859 0.39047
## stat197 -3.420e-02 7.177e-02 -0.477 0.63365
## stat198 -5.659e-02 7.222e-02 -0.784 0.43329
## stat199 1.024e-01 7.121e-02 1.439 0.15033
## stat200 -5.032e-02 7.104e-02 -0.708 0.47872
## stat201 -7.939e-03 7.201e-02 -0.110 0.91221
## stat202 -1.882e-02 7.275e-02 -0.259 0.79591
## stat203 -1.127e-02 7.208e-02 -0.156 0.87573
## stat204 -1.253e-01 7.163e-02 -1.749 0.08040 .
## stat205 -1.278e-03 7.202e-02 -0.018 0.98584
## stat206 -6.416e-02 7.246e-02 -0.885 0.37593
## stat207 1.168e-01 7.218e-02 1.618 0.10572
## stat208 3.622e-02 7.224e-02 0.501 0.61615
## stat209 1.313e-02 7.144e-02 0.184 0.85417
## stat210 -3.205e-02 7.248e-02 -0.442 0.65839
## stat211 -7.303e-02 7.219e-02 -1.012 0.31176
## stat212 -3.338e-03 7.209e-02 -0.046 0.96306
## stat213 -7.396e-02 7.262e-02 -1.018 0.30851
## stat214 -1.390e-01 7.195e-02 -1.932 0.05344 .
## stat215 -2.444e-02 7.236e-02 -0.338 0.73559
## stat216 -8.542e-02 7.194e-02 -1.187 0.23515
## stat217 6.822e-02 7.245e-02 0.942 0.34643
## sqrt.x18 7.334e+00 2.729e-01 26.876 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.482 on 5761 degrees of freedom
## Multiple R-squared: 0.2469, Adjusted R-squared: 0.2155
## F-statistic: 7.87 on 240 and 5761 DF, p-value: < 2.2e-16cd.full = plot.diagnostics(model.full, data.train)
## [1] "Number of data points that have Cook's D > 4/n: 281"
## [1] "Number of data points that have Cook's D > 1: 0"Just trial removing all high influence points
high.cd = names(cd.full[cd.full > 4/nrow(data.train)])
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)##
## Call:
## lm(formula = formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.342 -5.054 -0.875 4.696 20.836
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.501e+01 2.179e+00 39.007 < 2e-16 ***
## x1 -6.090e-02 1.506e-01 -0.404 0.686023
## x2 7.740e-02 9.539e-02 0.811 0.417167
## x3 5.034e-03 2.627e-02 0.192 0.848082
## x4 -1.622e-02 2.073e-03 -7.826 6.02e-15 ***
## x5 1.158e-01 6.762e-02 1.712 0.086950 .
## x6 -1.958e-01 1.365e-01 -1.434 0.151660
## x7 3.299e+00 1.465e-01 22.521 < 2e-16 ***
## x8 1.681e-01 3.403e-02 4.938 8.13e-07 ***
## x9 9.334e-01 7.596e-02 12.287 < 2e-16 ***
## x10 4.258e-01 7.072e-02 6.021 1.85e-09 ***
## x11 6.963e+07 1.691e+07 4.119 3.87e-05 ***
## x12 -4.005e-02 4.292e-02 -0.933 0.350773
## x13 3.333e-02 1.732e-02 1.925 0.054282 .
## x14 -1.075e-02 7.440e-02 -0.144 0.885128
## x15 2.399e-02 7.060e-02 0.340 0.734036
## x16 2.618e-01 4.927e-02 5.315 1.11e-07 ***
## x17 3.977e-01 7.453e-02 5.336 9.91e-08 ***
## x19 4.684e-02 3.819e-02 1.226 0.220100
## x20 9.046e-02 2.646e-01 0.342 0.732495
## x21 3.497e-02 9.678e-03 3.613 0.000305 ***
## x22 -8.333e-02 7.915e-02 -1.053 0.292467
## x23 1.554e-01 7.547e-02 2.059 0.039543 *
## stat1 -2.630e-03 5.677e-02 -0.046 0.963057
## stat2 -3.003e-02 5.660e-02 -0.531 0.595728
## stat3 1.126e-01 5.686e-02 1.980 0.047789 *
## stat4 -1.316e-01 5.726e-02 -2.298 0.021572 *
## stat5 -7.010e-02 5.694e-02 -1.231 0.218288
## stat6 -7.216e-03 5.732e-02 -0.126 0.899836
## stat7 -6.520e-02 5.691e-02 -1.146 0.251952
## stat8 -3.427e-02 5.677e-02 -0.604 0.546156
## stat9 -2.509e-02 5.702e-02 -0.440 0.659912
## stat10 -1.018e-01 5.717e-02 -1.781 0.075036 .
## stat11 -7.221e-02 5.722e-02 -1.262 0.207063
## stat12 5.257e-03 5.669e-02 0.093 0.926119
## stat13 -1.214e-01 5.672e-02 -2.140 0.032439 *
## stat14 -2.861e-01 5.637e-02 -5.076 3.98e-07 ***
## stat15 -1.452e-01 5.640e-02 -2.574 0.010066 *
## stat16 -2.433e-02 5.660e-02 -0.430 0.667280
## stat17 -1.634e-02 5.642e-02 -0.290 0.772077
## stat18 -2.582e-02 5.659e-02 -0.456 0.648229
## stat19 6.362e-02 5.704e-02 1.115 0.264782
## stat20 1.300e-02 5.711e-02 0.228 0.819953
## stat21 -2.467e-02 5.689e-02 -0.434 0.664586
## stat22 -6.038e-02 5.689e-02 -1.061 0.288628
## stat23 1.325e-01 5.639e-02 2.351 0.018770 *
## stat24 -6.822e-02 5.686e-02 -1.200 0.230257
## stat25 -7.183e-02 5.683e-02 -1.264 0.206309
## stat26 -1.614e-01 5.719e-02 -2.822 0.004785 **
## stat27 1.919e-02 5.694e-02 0.337 0.736182
## stat28 -2.941e-02 5.665e-02 -0.519 0.603702
## stat29 8.907e-02 5.691e-02 1.565 0.117609
## stat30 1.008e-02 5.710e-02 0.177 0.859838
## stat31 -8.743e-03 5.739e-02 -0.152 0.878923
## stat32 -5.232e-03 5.752e-02 -0.091 0.927532
## stat33 -9.703e-02 5.660e-02 -1.714 0.086535 .
## stat34 9.190e-02 5.695e-02 1.614 0.106618
## stat35 -1.266e-01 5.722e-02 -2.213 0.026962 *
## stat36 -3.697e-02 5.684e-02 -0.650 0.515432
## stat37 -4.131e-02 5.756e-02 -0.718 0.472903
## stat38 1.316e-01 5.686e-02 2.315 0.020651 *
## stat39 -1.005e-01 5.649e-02 -1.779 0.075345 .
## stat40 7.957e-03 5.706e-02 0.139 0.889099
## stat41 -1.423e-01 5.641e-02 -2.523 0.011662 *
## stat42 -4.363e-02 5.690e-02 -0.767 0.443207
## stat43 -9.442e-02 5.707e-02 -1.654 0.098099 .
## stat44 2.875e-02 5.696e-02 0.505 0.613804
## stat45 -6.909e-02 5.666e-02 -1.219 0.222722
## stat46 9.305e-02 5.723e-02 1.626 0.104014
## stat47 6.069e-02 5.718e-02 1.061 0.288607
## stat48 9.491e-02 5.736e-02 1.655 0.098029 .
## stat49 -6.226e-03 5.661e-02 -0.110 0.912433
## stat50 1.105e-01 5.642e-02 1.959 0.050211 .
## stat51 4.594e-02 5.702e-02 0.806 0.420500
## stat52 4.620e-02 5.716e-02 0.808 0.418979
## stat53 -7.150e-02 5.708e-02 -1.253 0.210403
## stat54 -1.575e-01 5.751e-02 -2.738 0.006195 **
## stat55 4.362e-02 5.640e-02 0.773 0.439311
## stat56 -4.732e-02 5.720e-02 -0.827 0.408139
## stat57 1.753e-02 5.648e-02 0.310 0.756265
## stat58 -1.203e-02 5.610e-02 -0.214 0.830236
## stat59 1.945e-02 5.653e-02 0.344 0.730766
## stat60 1.003e-01 5.702e-02 1.760 0.078547 .
## stat61 -7.257e-02 5.692e-02 -1.275 0.202371
## stat62 -1.293e-01 5.697e-02 -2.270 0.023249 *
## stat63 5.124e-02 5.710e-02 0.897 0.369532
## stat64 5.199e-02 5.636e-02 0.923 0.356299
## stat65 -3.579e-02 5.723e-02 -0.625 0.531732
## stat66 2.613e-02 5.747e-02 0.455 0.649391
## stat67 4.848e-02 5.702e-02 0.850 0.395310
## stat68 -8.471e-03 5.704e-02 -0.149 0.881938
## stat69 -5.434e-02 5.675e-02 -0.958 0.338308
## stat70 1.318e-01 5.639e-02 2.338 0.019441 *
## stat71 4.682e-02 5.692e-02 0.823 0.410759
## stat72 1.503e-02 5.722e-02 0.263 0.792824
## stat73 9.830e-02 5.723e-02 1.718 0.085932 .
## stat74 3.660e-02 5.714e-02 0.641 0.521837
## stat75 3.414e-02 5.707e-02 0.598 0.549751
## stat76 3.243e-02 5.710e-02 0.568 0.570085
## stat77 8.865e-03 5.712e-02 0.155 0.876662
## stat78 -5.318e-02 5.681e-02 -0.936 0.349241
## stat79 5.243e-02 5.687e-02 0.922 0.356624
## stat80 8.486e-02 5.738e-02 1.479 0.139226
## stat81 2.753e-02 5.706e-02 0.483 0.629446
## stat82 -9.852e-03 5.664e-02 -0.174 0.861934
## stat83 -1.178e-02 5.669e-02 -0.208 0.835434
## stat84 -1.012e-02 5.699e-02 -0.178 0.858992
## stat85 -7.021e-02 5.683e-02 -1.236 0.216697
## stat86 2.370e-03 5.679e-02 0.042 0.966713
## stat87 -1.324e-01 5.732e-02 -2.309 0.020958 *
## stat88 6.859e-03 5.648e-02 0.121 0.903345
## stat89 -3.643e-02 5.665e-02 -0.643 0.520280
## stat90 -5.824e-02 5.687e-02 -1.024 0.305823
## stat91 -1.114e-01 5.650e-02 -1.972 0.048689 *
## stat92 -9.709e-02 5.689e-02 -1.707 0.087968 .
## stat93 -1.413e-02 5.810e-02 -0.243 0.807906
## stat94 -5.150e-02 5.683e-02 -0.906 0.364871
## stat95 9.150e-02 5.706e-02 1.603 0.108904
## stat96 -3.346e-02 5.673e-02 -0.590 0.555305
## stat97 1.994e-02 5.653e-02 0.353 0.724349
## stat98 9.312e-01 5.585e-02 16.671 < 2e-16 ***
## stat99 1.299e-01 5.711e-02 2.275 0.022954 *
## stat100 1.440e-01 5.697e-02 2.528 0.011498 *
## stat101 2.342e-02 5.742e-02 0.408 0.683386
## stat102 -2.568e-02 5.736e-02 -0.448 0.654407
## stat103 -7.259e-02 5.725e-02 -1.268 0.204854
## stat104 -6.597e-02 5.673e-02 -1.163 0.244921
## stat105 3.897e-02 5.641e-02 0.691 0.489622
## stat106 -3.055e-02 5.647e-02 -0.541 0.588546
## stat107 7.915e-03 5.701e-02 0.139 0.889580
## stat108 -7.187e-02 5.678e-02 -1.266 0.205656
## stat109 -2.345e-02 5.674e-02 -0.413 0.679402
## stat110 -8.911e-01 5.656e-02 -15.755 < 2e-16 ***
## stat111 6.532e-02 5.703e-02 1.145 0.252112
## stat112 2.932e-02 5.729e-02 0.512 0.608883
## stat113 -3.761e-02 5.728e-02 -0.657 0.511503
## stat114 6.120e-02 5.668e-02 1.080 0.280227
## stat115 8.409e-02 5.655e-02 1.487 0.137100
## stat116 5.228e-02 5.708e-02 0.916 0.359757
## stat117 5.999e-03 5.704e-02 0.105 0.916234
## stat118 -1.050e-02 5.659e-02 -0.186 0.852745
## stat119 6.428e-02 5.697e-02 1.128 0.259228
## stat120 -2.677e-02 5.610e-02 -0.477 0.633248
## stat121 1.598e-02 5.691e-02 0.281 0.778952
## stat122 -5.615e-03 5.662e-02 -0.099 0.921008
## stat123 6.032e-02 5.743e-02 1.050 0.293679
## stat124 -4.183e-02 5.694e-02 -0.735 0.462581
## stat125 -1.929e-02 5.713e-02 -0.338 0.735663
## stat126 3.608e-02 5.667e-02 0.637 0.524341
## stat127 -1.269e-01 5.669e-02 -2.238 0.025288 *
## stat128 -1.597e-01 5.685e-02 -2.810 0.004974 **
## stat129 -2.988e-02 5.653e-02 -0.529 0.597116
## stat130 1.629e-02 5.709e-02 0.285 0.775344
## stat131 -1.952e-04 5.685e-02 -0.003 0.997260
## stat132 -1.482e-02 5.687e-02 -0.261 0.794412
## stat133 5.319e-02 5.721e-02 0.930 0.352580
## stat134 -5.205e-02 5.676e-02 -0.917 0.359183
## stat135 -4.344e-02 5.705e-02 -0.761 0.446442
## stat136 -1.358e-02 5.708e-02 -0.238 0.811961
## stat137 7.449e-02 5.628e-02 1.324 0.185661
## stat138 -4.539e-02 5.684e-02 -0.799 0.424573
## stat139 -1.047e-02 5.726e-02 -0.183 0.854939
## stat140 -3.594e-04 5.675e-02 -0.006 0.994947
## stat141 1.123e-01 5.673e-02 1.980 0.047774 *
## stat142 -6.705e-03 5.734e-02 -0.117 0.906925
## stat143 5.537e-02 5.730e-02 0.966 0.333912
## stat144 1.147e-01 5.668e-02 2.024 0.043022 *
## stat145 1.645e-02 5.788e-02 0.284 0.776271
## stat146 -1.537e-01 5.742e-02 -2.676 0.007471 **
## stat147 -7.457e-02 5.737e-02 -1.300 0.193744
## stat148 -4.924e-04 5.646e-02 -0.009 0.993042
## stat149 -9.743e-02 5.755e-02 -1.693 0.090479 .
## stat150 -3.768e-02 5.750e-02 -0.655 0.512258
## stat151 -6.100e-02 5.751e-02 -1.061 0.288882
## stat152 -5.377e-02 5.667e-02 -0.949 0.342682
## stat153 6.207e-02 5.787e-02 1.073 0.283498
## stat154 4.425e-02 5.730e-02 0.772 0.440001
## stat155 3.540e-02 5.709e-02 0.620 0.535271
## stat156 1.058e-01 5.702e-02 1.855 0.063587 .
## stat157 -1.379e-02 5.651e-02 -0.244 0.807227
## stat158 7.703e-03 5.760e-02 0.134 0.893625
## stat159 4.699e-02 5.694e-02 0.825 0.409181
## stat160 2.507e-02 5.745e-02 0.436 0.662622
## stat161 6.450e-02 5.720e-02 1.128 0.259514
## stat162 1.121e-02 5.644e-02 0.199 0.842605
## stat163 2.407e-02 5.760e-02 0.418 0.676114
## stat164 3.417e-02 5.731e-02 0.596 0.551089
## stat165 4.009e-02 5.704e-02 0.703 0.482195
## stat166 -1.385e-02 5.633e-02 -0.246 0.805738
## stat167 -1.128e-01 5.663e-02 -1.992 0.046475 *
## stat168 -2.459e-02 5.687e-02 -0.432 0.665512
## stat169 2.341e-03 5.703e-02 0.041 0.967258
## stat170 -4.428e-02 5.675e-02 -0.780 0.435235
## stat171 -2.599e-02 5.755e-02 -0.452 0.651625
## stat172 1.901e-01 5.675e-02 3.350 0.000814 ***
## stat173 -7.634e-03 5.723e-02 -0.133 0.893890
## stat174 3.762e-02 5.726e-02 0.657 0.511200
## stat175 -9.638e-02 5.700e-02 -1.691 0.090918 .
## stat176 -2.919e-02 5.719e-02 -0.510 0.609749
## stat177 -5.016e-02 5.704e-02 -0.880 0.379168
## stat178 -8.780e-03 5.755e-02 -0.153 0.878747
## stat179 7.833e-03 5.654e-02 0.139 0.889818
## stat180 3.653e-02 5.657e-02 0.646 0.518483
## stat181 2.599e-02 5.711e-02 0.455 0.649087
## stat182 3.979e-02 5.729e-02 0.694 0.487432
## stat183 8.976e-02 5.682e-02 1.580 0.114233
## stat184 7.092e-02 5.729e-02 1.238 0.215819
## stat185 4.818e-03 5.618e-02 0.086 0.931658
## stat186 4.293e-02 5.744e-02 0.747 0.454900
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## stat188 6.155e-02 5.675e-02 1.085 0.278159
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## stat193 3.384e-02 5.746e-02 0.589 0.555930
## stat194 -9.998e-02 5.691e-02 -1.757 0.079042 .
## stat195 2.392e-02 5.701e-02 0.420 0.674770
## stat196 -6.266e-02 5.760e-02 -1.088 0.276696
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## stat199 7.190e-02 5.618e-02 1.280 0.200623
## stat200 -1.339e-02 5.620e-02 -0.238 0.811767
## stat201 4.254e-02 5.696e-02 0.747 0.455148
## stat202 -1.272e-03 5.733e-02 -0.022 0.982293
## stat203 4.000e-02 5.685e-02 0.704 0.481637
## stat204 -3.884e-02 5.652e-02 -0.687 0.491981
## stat205 6.371e-02 5.658e-02 1.126 0.260163
## stat206 -6.731e-02 5.719e-02 -1.177 0.239302
## stat207 1.075e-01 5.691e-02 1.889 0.058893 .
## stat208 4.630e-02 5.703e-02 0.812 0.416851
## stat209 1.204e-02 5.627e-02 0.214 0.830522
## stat210 -6.352e-02 5.718e-02 -1.111 0.266663
## stat211 -2.286e-02 5.690e-02 -0.402 0.687844
## stat212 2.164e-02 5.688e-02 0.380 0.703694
## stat213 -5.703e-02 5.725e-02 -0.996 0.319233
## stat214 -8.715e-02 5.683e-02 -1.533 0.125244
## stat215 -2.077e-02 5.710e-02 -0.364 0.716015
## stat216 -8.613e-02 5.669e-02 -1.519 0.128786
## stat217 4.368e-02 5.721e-02 0.764 0.445191
## sqrt.x18 7.173e+00 2.146e-01 33.425 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.297 on 5480 degrees of freedom
## Multiple R-squared: 0.3513, Adjusted R-squared: 0.3229
## F-statistic: 12.37 on 240 and 5480 DF, p-value: < 2.2e-16cd.full2 = plot.diagnostics(model.full2, data.train2)
## [1] "Number of data points that have Cook's D > 4/n: 311"
## [1] "Number of data points that have Cook's D > 1: 0"# much more normal residuals than before.
# See if you can check the distribution (boxplots) of the high leverage points and the other pointsmodel.null = lm(grand.mean.formula, data.train)
summary(model.null)##
## Call:
## lm(formula = grand.mean.formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.346 -7.106 -1.444 5.673 68.468
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 125.2584 0.1382 906.4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.71 on 6001 degrees of freedomplot.diagnostics(model.null, data.train)
## hat values (leverages) are all = 0.0001666111
## and there are no factor predictors; no plot no. 5
## Warning in plot.window(...): relative range of values = 32 * EPS, is small
## (axis 2)
## [1] "Number of data points that have Cook's D > 4/n: 282"
## [1] "Number of data points that have Cook's D > 1: 0"## 2689 2932 173 4452 7385
## 2.745583e-04 9.331561e-05 9.057318e-05 2.913857e-04 1.082908e-04
## 9881 3952 756 9468 8265
## 2.064267e-04 1.037350e-05 8.905355e-05 6.296671e-08 8.223854e-05
## 7775 3239 5947 2569 8467
## 2.116619e-05 2.402808e-06 1.442083e-04 1.120538e-03 1.840443e-07
## 7082 5633 3086 5522 4138
## 3.443192e-07 1.392294e-05 6.656586e-05 2.529151e-05 7.376404e-07
## 2063 8461 4679 7746 427
## 5.168752e-05 5.756294e-05 4.565436e-07 9.189593e-05 3.072196e-05
## 3969 3017 7362 2616 3755
## 7.493143e-08 6.556577e-07 2.358264e-04 2.076915e-04 1.809545e-04
## 4718 8312 3452 6027 3293
## 7.917503e-05 6.944143e-06 4.191343e-06 3.316992e-05 7.977664e-07
## 3639 5815 2208 7079 2625
## 8.379344e-05 9.883538e-05 5.755758e-04 1.989042e-04 1.961714e-04
## 3341 1938 9416 2433 1432
## 1.355196e-05 1.005664e-04 3.339736e-05 1.520553e-06 6.196421e-05
## 8296 167 9527 5785 7
## 1.761362e-05 2.974843e-05 1.239959e-04 1.069824e-04 1.138771e-03
## 9962 5854 143 2754 4668
## 6.858710e-05 2.186615e-06 1.013194e-06 9.006593e-05 6.122227e-06
## 2752 6784 4555 611 5716
## 2.885233e-05 3.977634e-05 1.478880e-04 1.232881e-04 2.072512e-06
## 1086 8052 9675 950 2339
## 8.425678e-06 7.347671e-06 1.646092e-04 1.541297e-04 1.367022e-05
## 352 2155 5945 9245 2909
## 1.128592e-04 1.397340e-04 1.962199e-04 6.789938e-08 1.245938e-07
## 5238 7521 8596 4129 2669
## 9.621965e-06 3.057784e-04 2.618969e-04 3.484402e-04 2.974192e-06
## 5919 2016 8599 3309 1958
## 3.325782e-04 2.714680e-04 2.502291e-04 1.578725e-04 1.561673e-05
## 1438 2206 6261 6462 623
## 1.999199e-04 1.357197e-04 2.041838e-03 6.342242e-04 2.520159e-04
## 6643 1673 5777 8908 7184
## 2.471551e-05 1.599488e-04 2.219173e-04 1.063960e-07 5.808524e-05
## 2943 6118 8711 2104 2082
## 1.407222e-05 2.618408e-06 9.147214e-04 6.552030e-07 6.649267e-04
## 2663 67 1458 9256 5808
## 1.046132e-04 2.354162e-04 4.148164e-05 1.003956e-05 6.633921e-05
## 1017 6976 5582 1371 8657
## 3.259080e-06 1.046325e-04 4.902478e-05 1.446916e-04 2.519451e-05
## 2085 8652 438 5379 7528
## 5.148210e-04 6.879983e-05 5.867120e-06 1.081995e-04 3.011548e-04
## 1679 8994 2196 2956 3982
## 1.452067e-04 2.424238e-05 3.582835e-05 6.116010e-06 2.723614e-05
## 586 4827 9197 2918 4522
## 1.180716e-03 4.675224e-04 9.199069e-05 3.526093e-05 1.343950e-04
## 17 4012 4051 1395 1542
## 9.657027e-06 2.375046e-06 2.469538e-05 2.720902e-06 6.574806e-05
## 7802 7192 3690 7044 7072
## 2.155488e-04 8.116802e-05 2.478411e-05 1.051830e-05 1.104231e-05
## 4985 6191 816 6005 311
## 1.346818e-07 9.396574e-07 3.886747e-04 1.881372e-04 3.938049e-05
## 8448 550 7601 4753 1663
## 3.867360e-05 5.593104e-04 2.112664e-04 3.811205e-04 2.037254e-05
## 5955 7307 2575 5151 7969
## 3.024098e-04 5.850712e-05 3.401438e-05 3.171959e-04 4.952485e-05
## 4819 7942 1786 319 8423
## 2.819961e-05 1.861899e-06 1.275620e-04 1.231803e-03 1.873197e-04
## 5697 7027 3073 9669 1720
## 2.039541e-06 9.294315e-06 1.406660e-04 2.249174e-04 2.571899e-05
## 400 1210 4441 3060 2734
## 1.009970e-03 2.934413e-05 1.485160e-04 4.255836e-06 7.738112e-05
## 6687 5231 2311 7499 629
## 2.390804e-05 1.571311e-04 5.570538e-05 1.665351e-04 5.344374e-05
## 5658 3622 4591 3699 964
## 7.934181e-05 1.173890e-05 3.730760e-04 4.225039e-06 1.131966e-05
## 6177 8861 689 4206 5004
## 5.040074e-07 3.488872e-06 7.635962e-05 1.780521e-04 1.823522e-04
## 5906 7834 6096 51 5683
## 1.072157e-05 4.668606e-07 7.500762e-05 3.227863e-05 2.856827e-04
## 5307 6700 2061 1839 8960
## 2.173180e-05 3.598907e-05 1.140758e-04 9.027017e-05 1.026107e-05
## 5074 5482 6212 9973 4139
## 7.111047e-05 1.537234e-04 3.211394e-05 3.761165e-09 2.020147e-03
## 2755 7108 8983 1466 3097
## 4.834247e-05 2.973757e-05 3.028200e-05 1.335302e-03 1.439140e-04
## 605 1732 7466 3675 2725
## 1.332623e-06 1.686053e-04 1.654758e-04 1.530207e-04 6.889275e-05
## 401 5200 9727 6001 53
## 2.795489e-04 2.287372e-06 5.625362e-05 9.485055e-05 1.312405e-04
## 7696 349 6129 8113 891
## 3.988344e-06 1.850200e-04 8.542980e-05 2.474390e-04 1.983492e-04
## 9427 1611 562 8692 5552
## 3.588472e-04 5.161617e-07 5.496195e-04 8.182428e-04 5.701920e-05
## 8519 9812 823 8915 9784
## 1.757111e-04 9.189975e-05 9.468378e-07 4.306754e-04 4.471053e-05
## 4764 643 1722 7095 4748
## 6.998847e-05 1.185035e-04 7.177731e-05 5.014681e-06 1.289990e-04
## 222 799 1584 2362 6152
## 3.218564e-05 1.628332e-05 1.045378e-04 7.162086e-05 6.299747e-05
## 2499 6519 7494 7404 4205
## 5.223504e-04 5.119614e-08 4.575420e-04 8.986188e-05 7.902563e-06
## 4867 7645 8212 5404 530
## 4.626852e-05 7.029976e-05 4.382542e-05 2.636731e-04 5.174510e-06
## 283 2483 7709 4882 7554
## 1.515418e-05 1.722634e-04 1.774433e-05 5.461377e-05 4.616089e-04
## 6767 7268 174 4649 984
## 1.439263e-03 1.632262e-04 5.993945e-04 1.917508e-04 3.294715e-08
## 4822 6506 4182 8190 7127
## 7.908909e-05 1.296095e-05 5.520637e-05 3.836087e-04 2.754344e-04
## 1436 3038 2017 811 3784
## 6.626821e-04 2.511788e-05 2.589617e-04 7.396820e-05 8.509531e-05
## 9042 2423 3194 220 6852
## 5.320712e-04 5.410006e-05 6.204918e-04 4.566861e-05 1.066748e-05
## 7435 5548 4204 5165 2790
## 3.394608e-04 1.395103e-04 1.447426e-05 5.592713e-05 6.528489e-05
## 2386 6721 7459 509 992
## 5.104549e-06 1.284197e-04 6.899621e-05 2.811043e-05 6.417449e-05
## 2922 77 7284 8004 8443
## 2.319123e-04 2.113199e-04 6.551677e-05 2.750963e-04 2.017050e-04
## 1776 2954 8580 2821 2144
## 1.221997e-05 2.870100e-05 1.037025e-06 9.762847e-05 3.917830e-05
## 8843 1230 4435 7628 7312
## 3.800929e-06 4.198270e-09 3.758943e-04 3.385221e-04 5.758117e-04
## 9632 7807 884 9583 5396
## 4.447281e-05 5.195593e-05 1.146196e-05 1.526593e-04 5.627487e-05
## 3633 7178 2175 9067 6579
## 5.711101e-06 1.231135e-05 1.137033e-04 2.662619e-05 1.531694e-05
## 8752 8751 2115 1727 7900
## 1.329440e-04 2.736223e-04 1.145895e-04 1.663683e-05 5.422732e-07
## 6814 3694 468 1934 2198
## 7.697421e-05 2.182319e-03 1.216490e-06 5.271961e-08 2.190648e-05
## 6858 1764 4314 272 55
## 1.081533e-06 1.384308e-04 6.981640e-06 5.850090e-06 4.100864e-05
## 9350 8588 5355 6595 3371
## 3.535506e-05 1.450408e-05 4.079994e-03 2.185891e-04 3.024083e-05
## 3211 8473 7444 4074 6783
## 5.790547e-05 3.393514e-04 5.900883e-04 2.509397e-04 6.594637e-04
## 5348 3821 8566 1941 4611
## 6.486657e-07 7.928363e-05 3.269600e-05 1.117759e-05 3.340975e-04
## 7730 9048 3498 5645 1771
## 1.015763e-06 2.453165e-05 1.897450e-04 3.186547e-04 2.919006e-06
## 5113 7344 3656 3708 6503
## 7.607254e-06 7.938968e-04 8.433936e-06 1.774181e-06 2.542467e-05
## 9504 5232 6440 9094 8998
## 5.280075e-05 5.876396e-04 1.836548e-04 1.159980e-05 6.358870e-05
## 5631 6446 3439 699 6934
## 4.224533e-06 3.073841e-05 7.459152e-06 2.976387e-05 1.676712e-05
## 4348 5700 2394 3312 7166
## 1.395181e-05 1.139547e-04 2.964847e-07 7.101844e-06 1.663700e-04
## 1278 5530 8343 3046 2808
## 3.703122e-05 4.048312e-05 3.752632e-06 1.504906e-04 1.087499e-04
## 6332 4337 8717 7699 3175
## 9.205940e-05 2.543605e-05 1.466992e-04 2.198474e-05 8.300433e-07
## 2516 4437 2972 5639 8202
## 2.895944e-05 1.492410e-07 5.608631e-05 4.684376e-04 1.831322e-04
## 6017 8950 1452 1194 8606
## 3.636165e-05 2.001615e-05 3.885382e-06 1.956850e-06 5.948944e-05
## 6139 8182 5662 2165 7909
## 1.233987e-04 2.123563e-04 2.308344e-04 2.034372e-04 1.362991e-03
## 4673 8791 2865 9095 5357
## 5.710781e-05 3.979191e-04 4.849823e-05 5.488302e-06 2.307855e-04
## 2854 2126 5764 5015 5365
## 9.325367e-06 1.309316e-04 1.411648e-06 1.028394e-07 2.307406e-04
## 7454 2418 8124 4214 5626
## 1.037068e-04 9.789902e-05 2.875919e-04 1.174205e-04 1.747547e-04
## 1615 2182 5708 871 5371
## 6.812797e-05 1.584397e-05 2.298943e-04 5.111579e-06 1.133764e-03
## 2613 9278 6116 261 1281
## 3.813206e-04 1.313897e-03 1.337566e-04 1.616955e-04 1.062921e-06
## 2822 5846 2360 8903 1740
## 3.513488e-05 1.096456e-04 1.174699e-04 4.484299e-04 3.662688e-05
## 7798 5930 1955 7073 6380
## 2.142790e-05 1.081200e-07 9.241971e-06 2.420545e-05 1.266866e-05
## 6962 7944 8278 8345 8183
## 5.642045e-06 1.656720e-07 1.040116e-05 7.471365e-06 6.927689e-04
## 7363 7917 5810 6560 7879
## 1.235474e-07 2.315609e-04 6.159549e-07 9.499769e-04 2.800605e-04
## 745 7203 2914 7655 2021
## 1.171120e-04 1.929792e-03 3.161364e-05 2.809296e-04 3.311028e-05
## 5547 2319 6318 7703 4312
## 5.765809e-05 2.694609e-05 3.519341e-05 9.081601e-05 3.412493e-10
## 7822 3484 5466 4360 6289
## 6.961662e-05 1.493270e-05 5.004405e-08 1.353122e-04 1.046059e-04
## 8101 4624 9838 4600 1126
## 1.152191e-04 2.286385e-05 1.830664e-05 5.782421e-08 7.815239e-04
## 3247 4791 4698 5440 6019
## 6.171424e-04 5.245463e-06 6.650019e-06 1.184281e-05 3.592472e-04
## 9643 688 196 835 10
## 1.260765e-05 7.795769e-05 8.314096e-04 3.059122e-05 1.239998e-07
## 2222 8454 8033 129 2966
## 3.178706e-04 1.267747e-04 5.392467e-06 3.499352e-04 8.583070e-05
## 259 7356 6714 8856 3509
## 1.113616e-03 7.785483e-04 2.811742e-04 4.211470e-06 8.383764e-06
## 9677 8171 6153 2290 3347
## 6.805496e-05 4.283545e-04 8.583553e-08 3.030266e-04 2.813892e-04
## 9228 7341 4625 5760 765
## 7.704337e-05 1.321489e-04 8.037780e-05 5.060204e-05 6.787376e-07
## 4844 9169 7967 3241 7230
## 1.611827e-04 1.438845e-04 4.956661e-05 5.206194e-04 6.018258e-04
## 3802 2744 8790 4449 7471
## 2.889467e-04 7.281901e-07 9.673534e-05 3.331886e-04 5.680962e-07
## 4398 1073 2946 1028 7658
## 2.385753e-05 8.242090e-04 2.943956e-03 1.256748e-04 1.813922e-06
## 2108 7199 4535 3636 2662
## 4.339294e-04 4.005303e-04 3.059098e-05 1.266729e-04 1.135800e-04
## 8651 1831 1322 282 4912
## 1.125758e-05 1.126971e-04 1.285355e-04 4.370518e-05 7.442651e-05
## 9405 6014 6792 8299 9298
## 1.960192e-04 1.259791e-07 1.952000e-04 2.443116e-05 5.759097e-05
## 6200 6580 3440 8681 1810
## 1.327832e-04 9.912896e-05 5.598759e-04 1.365715e-07 1.657386e-03
## 5984 1900 9975 4465 4127
## 6.726913e-05 3.904557e-04 5.262858e-04 5.310730e-05 9.678421e-05
## 8822 9888 8509 7593 4831
## 3.827389e-04 7.104034e-05 3.707171e-06 1.449373e-04 5.867975e-05
## 8111 3419 4984 9289 4208
## 6.853647e-04 1.596390e-08 4.882369e-05 3.959000e-05 3.805989e-07
## 4792 3043 7886 322 4796
## 4.331051e-04 2.818946e-05 1.758027e-05 1.223905e-04 1.486936e-05
## 5775 7419 1355 3672 2703
## 1.809833e-04 1.971470e-04 3.623970e-05 3.072882e-05 1.259265e-05
## 7352 1601 6848 8910 1189
## 8.108087e-05 8.179571e-05 2.171156e-04 1.698634e-04 9.840391e-05
## 1905 7697 4928 1196 7842
## 3.672885e-06 1.487334e-04 1.575000e-05 1.159415e-04 4.128560e-06
## 6608 8187 3089 630 5887
## 9.562393e-06 3.488435e-05 6.851781e-05 5.972858e-05 9.663588e-07
## 9721 5037 2791 4675 4648
## 9.452746e-05 6.978697e-05 7.451477e-06 5.424652e-05 1.110868e-07
## 7174 8708 5358 5844 3388
## 2.788916e-05 1.409217e-04 2.161241e-04 5.412351e-04 2.403790e-04
## 9977 8949 2013 5115 9149
## 1.244646e-05 5.012332e-05 1.703411e-04 7.271062e-06 3.916128e-04
## 108 6084 3678 5061 4557
## 3.387083e-05 3.904777e-06 2.559812e-04 1.010729e-04 1.603120e-04
## 182 5894 9665 1176 1757
## 5.840314e-04 1.533414e-05 6.488882e-07 3.463455e-05 1.975387e-05
## 6505 1967 6481 9240 8530
## 9.568496e-05 2.282854e-05 4.632618e-04 2.456590e-05 6.524739e-05
## 1918 2103 209 1036 7580
## 1.097881e-03 4.853396e-05 7.641903e-05 1.908785e-05 1.633450e-04
## 6888 3279 9440 6355 5008
## 5.049403e-05 9.788850e-06 4.686891e-08 1.552566e-04 1.366362e-05
## 589 4147 7991 3098 6053
## 8.535672e-05 4.536646e-04 7.354687e-05 2.918402e-08 1.245219e-04
## 6789 4652 1627 294 6625
## 3.381236e-04 3.416646e-04 4.273895e-05 5.460501e-05 2.829160e-10
## 5020 8797 2917 146 954
## 1.509274e-04 1.279614e-06 2.140091e-04 1.723170e-06 2.372765e-04
## 508 5247 6066 8639 2383
## 5.158921e-04 1.788015e-05 9.748692e-05 5.353219e-05 3.720756e-04
## 439 7217 7398 9191 8559
## 5.301142e-05 1.600644e-05 1.392994e-04 1.785849e-04 1.996199e-05
## 9476 7866 2834 3993 9907
## 3.624168e-06 6.983602e-06 1.544090e-05 4.068125e-05 1.856058e-05
## 3958 2275 5445 9876 2517
## 6.301943e-04 3.236319e-05 6.514585e-05 1.059803e-05 5.067717e-06
## 690 364 5638 5471 8242
## 6.201452e-07 3.177681e-05 2.159828e-05 2.600239e-04 3.379903e-05
## 3934 6339 9362 9924 2523
## 6.342283e-06 8.890797e-05 8.517158e-06 1.700827e-04 4.797486e-05
## 7161 659 5907 243 913
## 3.273396e-05 1.809496e-05 9.159960e-05 5.612120e-04 1.151409e-04
## 8382 6150 8282 4908 9960
## 1.745018e-04 3.595215e-06 2.103646e-05 1.969416e-06 4.165827e-05
## 4692 4929 1492 5723 3183
## 6.768437e-06 8.702567e-05 5.927507e-05 3.236078e-04 3.799326e-05
## 8128 2341 7291 9769 7198
## 2.005051e-04 2.685157e-04 1.905885e-04 8.590273e-05 2.300348e-07
## 4125 9868 5573 1830 4694
## 1.327168e-04 2.812045e-05 1.492007e-04 1.848342e-06 1.423505e-04
## 435 4561 6864 5568 1061
## 4.774027e-04 1.100480e-04 1.728336e-04 1.006262e-04 2.015355e-04
## 6981 1358 1286 2693 1276
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## 7370 3856 887 3833 3818
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## 8402 91 4907 1991 7461
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## 1.471242e-05 7.247130e-05 9.513190e-05 1.584806e-03 2.793873e-06
## 4958 7010 6486 9698 5164
## 2.199577e-05 5.153430e-06 6.146518e-04 5.049788e-04 1.656611e-09
## 5401 7160 1172 5605 4209
## 2.200480e-04 2.140921e-04 4.411194e-04 7.488342e-06 3.991025e-04
## 1875 7436 271 6028 9571
## 7.216326e-05 6.045453e-06 3.210810e-05 3.833108e-04 2.904764e-04
## 5359 5834 3659 5398 5069
## 5.260805e-04 9.339771e-05 2.593118e-05 1.728099e-04 5.197529e-05
## 1642 714 8785 1233 4361
## 1.056332e-03 8.813760e-06 1.187110e-04 1.633516e-05 2.508847e-09
## 1837 6620 4388 8931 6599
## 4.376553e-04 6.515172e-05 6.267008e-05 6.298532e-04 6.019672e-06
## 1693 3074 3927 7034 1817
## 5.064210e-05 1.128494e-05 4.695161e-05 5.920131e-07 3.075620e-05
## 4462 8698 6782 7460 3782
## 1.639239e-06 3.532911e-04 4.068075e-04 8.205453e-07 1.008949e-08
## 315 8169
## 3.011843e-06 6.962800e-07model.null2 = lm(grand.mean.formula, data.train2)
summary(model.null2)##
## Call:
## lm(formula = grand.mean.formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.0593 -6.1322 -0.6858 5.7872 29.7528
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 124.0164 0.1172 1058 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.868 on 5720 degrees of freedomplot.diagnostics(model.null2, data.train2)
## hat values (leverages) are all = 0.0001747946
## and there are no factor predictors; no plot no. 5
## Warning in plot.window(...): relative range of values = 52 * EPS, is small
## (axis 2)
## [1] "Number of data points that have Cook's D > 4/n: 266"
## [1] "Number of data points that have Cook's D > 1: 0"## 2689 2932 173 4452 7385
## 4.991973e-04 1.018851e-04 9.834627e-05 3.708422e-04 2.167002e-04
## 9881 3952 756 9468 8265
## 3.849195e-04 3.404665e-05 9.638962e-05 2.376885e-06 1.707322e-04
## 7775 3239 5947 8467 7082
## 1.472489e-05 1.420478e-05 2.789669e-04 5.676512e-06 1.268746e-06
## 5633 3086 5522 4138 2063
## 4.181324e-05 6.785433e-05 1.907127e-05 8.492071e-06 1.154045e-04
## 8461 4679 7746 427 3969
## 1.262109e-04 7.223141e-06 1.000519e-04 2.502290e-05 4.798441e-06
## 3017 7362 2616 3755 4718
## 8.141643e-06 2.937263e-04 3.870550e-04 2.185379e-04 1.652663e-04
## 8312 3452 6027 3293 3639
## 1.978830e-06 4.619895e-07 8.053598e-05 8.741212e-06 8.964161e-05
## 5815 7079 2625 3341 1938
## 1.090363e-04 2.430038e-04 2.392699e-04 4.101668e-05 2.031563e-04
## 9416 2433 1432 8296 167
## 2.803185e-05 1.070128e-07 1.342456e-04 4.958951e-05 7.390604e-05
## 9527 5785 9962 5854 143
## 1.420452e-04 2.144106e-04 7.038218e-05 1.354721e-05 9.590079e-06
## 2754 4668 2752 6784 4555
## 1.846342e-04 2.412610e-05 2.294842e-05 3.536930e-05 1.738845e-04
## 611 5716 1086 8052 9675
## 1.411085e-04 1.319363e-05 3.019050e-06 2.708270e-05 1.963906e-04
## 950 2339 352 2155 5945
## 1.822663e-04 4.127094e-05 2.246815e-04 1.629723e-04 3.676630e-04
## 9245 2909 5238 7521 8596
## 4.727403e-06 5.237360e-06 3.935907e-06 5.511398e-04 3.298085e-04
## 4129 2669 5919 2016 8599
## 6.217856e-04 7.876280e-08 5.955598e-04 4.940431e-04 3.136355e-04
## 3309 1958 1438 2206 6462
## 3.024101e-04 4.541326e-05 2.443922e-04 2.643423e-04 1.088674e-03
## 623 6643 1673 5777 8908
## 4.615419e-04 6.399823e-05 3.059625e-04 2.745617e-04 5.086798e-06
## 7184 2943 6118 2104 2082
## 5.734701e-05 7.767023e-06 2.220889e-08 8.139661e-06 1.138385e-03
## 2663 67 1458 9256 5808
## 1.165599e-04 2.931603e-04 3.736436e-05 3.329657e-05 6.757141e-05
## 1017 6976 5582 1371 8657
## 1.447443e-07 1.165852e-04 4.632938e-05 2.797982e-04 6.495034e-05
## 2085 8652 438 5379 7528
## 8.946517e-04 7.064871e-05 2.349733e-05 1.212481e-04 5.434612e-04
## 1679 8994 2196 2956 3982
## 1.702913e-04 6.305567e-05 3.080296e-05 1.454990e-06 2.117590e-05
## 4827 9197 2918 4522 17
## 6.193479e-04 1.001742e-04 3.015320e-05 1.558521e-04 3.963661e-06
## 4012 4051 1395 1542 7802
## 2.890951e-09 1.843274e-05 3.527435e-08 1.411167e-04 2.658088e-04
## 7192 3690 7044 7072 4985
## 8.628879e-05 1.852757e-05 3.437067e-05 5.095366e-06 5.316969e-06
## 6191 816 6005 311 8448
## 9.307151e-06 5.075070e-04 3.539672e-04 3.490805e-05 3.408619e-05
## 7601 4753 1663 5955 7307
## 2.599315e-04 4.968366e-04 1.391006e-05 5.455459e-04 1.279386e-04
## 2575 5151 7969 4819 7942
## 8.216107e-05 4.069231e-04 4.693095e-05 7.087845e-05 1.252751e-05
## 1786 8423 5697 7027 3073
## 2.502385e-04 2.271976e-04 7.389695e-09 3.678858e-06 1.642174e-04
## 9669 1720 1210 4441 3060
## 2.786900e-04 1.953113e-05 2.349170e-05 1.747267e-04 4.887434e-07
## 2734 6687 5231 2311 7499
## 1.620586e-04 1.759450e-05 1.863052e-04 5.443026e-05 1.989930e-04
## 629 5658 3622 4591 3699
## 1.186450e-04 8.396294e-05 5.687868e-06 4.854833e-04 4.758993e-07
## 964 6177 8861 689 4206
## 5.329532e-06 9.488676e-07 1.732112e-05 8.017653e-05 2.145956e-04
## 5004 5906 7834 6096 51
## 3.441471e-04 4.827557e-06 1.014191e-06 7.846492e-05 2.676817e-05
## 5683 5307 6700 2061 1839
## 5.177317e-04 5.801664e-05 8.594538e-05 1.289576e-04 9.795587e-05
## 8960 5074 5482 6212 9973
## 4.448973e-06 1.508021e-04 1.817199e-04 7.849781e-05 3.716663e-06
## 2755 7108 8983 3097 605
## 4.550992e-05 2.392758e-05 2.453253e-05 2.784608e-04 1.075565e-05
## 1732 7466 3675 2725 401
## 2.017926e-04 1.975614e-04 1.807753e-04 7.076516e-05 5.075159e-04
## 5200 9727 6001 53 7696
## 1.385559e-05 5.510083e-05 1.930908e-04 1.516550e-04 3.814640e-07
## 349 6129 8113 891 9427
## 3.486776e-04 9.173659e-05 4.538792e-04 3.712666e-04 4.654274e-04
## 1611 562 8692 5552 8519
## 9.284781e-07 9.513226e-04 1.123703e-03 5.603861e-05 2.114188e-04
## 9812 823 8915 9784 4764
## 1.000569e-04 9.335065e-06 5.669826e-04 4.117548e-05 7.213964e-05
## 643 1722 7095 4748 222
## 1.347883e-04 7.438860e-05 2.135612e-05 2.527267e-04 7.863640e-05
## 799 1584 2362 6152 2499
## 4.681494e-05 1.164615e-04 7.419167e-05 6.341285e-05 6.975473e-04
## 6519 7404 4205 4867 7645
## 2.471869e-06 9.743002e-05 2.638433e-06 1.053435e-04 7.253056e-05
## 8212 5404 530 283 2483
## 1.007736e-04 4.810314e-04 2.176272e-05 4.443582e-05 3.269832e-04
## 7709 4882 7554 7268 174
## 4.986060e-05 1.207989e-04 6.109331e-04 1.945231e-04 1.032198e-03
## 4649 984 4822 6506 4182
## 2.332367e-04 4.311808e-06 1.651128e-04 6.760018e-06 1.218883e-04
## 8190 7127 3038 2017 811
## 6.797784e-04 5.006582e-04 6.479817e-05 3.257364e-04 1.559408e-04
## 3784 9042 2423 3194 220
## 1.758163e-04 9.227585e-04 5.247151e-05 1.066418e-03 4.231420e-05
## 6852 7435 5548 4204 5165
## 4.782718e-06 4.381571e-04 2.708791e-04 8.138111e-06 5.470139e-05
## 2790 2386 6721 7459 509
## 1.402773e-04 2.158505e-05 1.479083e-04 7.089483e-05 2.213226e-05
## 992 2922 77 7284 8004
## 1.382632e-04 4.278378e-04 2.600049e-04 1.406976e-04 5.000944e-04
## 8443 1776 2954 8580 2821
## 2.468337e-04 3.812962e-05 7.186049e-05 9.680429e-06 1.979875e-04
## 2144 8843 1230 4435 7628
## 9.201423e-05 1.817277e-05 3.733206e-06 4.894596e-04 6.053926e-04
## 7312 9632 7807 884 9583
## 9.939060e-04 4.089347e-05 1.159004e-04 5.450583e-06 2.934794e-04
## 5396 3633 7178 2175 9067
## 1.238501e-04 1.217185e-06 3.832912e-05 1.284679e-04 2.051232e-05
## 6579 8752 8751 2115 1727
## 4.478023e-05 1.539206e-04 4.976364e-04 1.296332e-04 4.755511e-05
## 7900 6814 468 1934 2198
## 7.632336e-06 8.095564e-05 1.034240e-05 2.458891e-06 5.836943e-05
## 6858 1764 4314 272 55
## 9.847541e-06 2.690185e-04 2.003627e-06 1.297334e-06 9.547536e-05
## 9350 8588 6595 3371 3211
## 8.473270e-05 8.165777e-06 2.699856e-04 7.486497e-05 5.712617e-05
## 8473 7444 4074 5348 3821
## 6.067640e-04 1.017093e-03 4.597406e-04 8.111121e-06 8.388893e-05
## 8566 1941 4611 7730 9048
## 2.723872e-05 5.209283e-06 5.980738e-04 3.668562e-07 6.363219e-05
## 3498 5645 1771 5113 7344
## 2.305019e-04 5.724999e-04 1.571978e-05 2.769709e-05 1.346560e-03
## 3656 3708 6503 9504 5232
## 3.025165e-06 4.196525e-08 1.921434e-05 5.089158e-05 7.910409e-04
## 6440 9094 8998 5631 6446
## 2.222094e-04 5.568402e-06 6.414679e-05 4.756893e-07 2.504126e-05
## 3439 699 6934 4348 5700
## 2.326812e-06 7.393613e-05 4.782736e-05 4.187509e-05 1.287984e-04
## 2394 3312 7166 1278 5530
## 1.389274e-06 2.649730e-05 3.169334e-04 8.793411e-05 9.448315e-05
## 8343 3046 2808 6332 4337
## 2.954334e-07 2.897595e-04 1.219687e-04 1.881611e-04 1.922657e-05
## 8717 7699 3175 2516 4437
## 1.722908e-04 1.557304e-05 8.872515e-06 7.236596e-05 1.888682e-06
## 2972 5639 8202 6017 8950
## 1.235041e-04 6.206507e-04 2.214985e-04 8.665703e-05 5.453277e-05
## 1452 1194 8606 6139 8182
## 3.428589e-07 1.491699e-08 5.907494e-05 1.412548e-04 3.949259e-04
## 5662 2165 4673 8791 2865
## 2.868407e-04 2.492039e-04 5.614725e-05 7.033205e-04 1.094951e-04
## 9095 5357 2854 2126 5764
## 1.092114e-06 4.259449e-04 3.703037e-06 2.560702e-04 1.464983e-07
## 5015 5365 7454 2418 8124
## 5.056174e-06 2.867114e-04 1.153772e-04 1.984639e-04 5.209095e-04
## 4214 5626 1615 2182 5708
## 1.333605e-04 3.312262e-04 6.980723e-05 9.426831e-06 2.855451e-04
## 871 2613 6116 261 1281
## 2.160293e-05 6.760113e-04 2.609529e-04 1.924572e-04 9.777910e-06
## 2822 5846 2360 1740 7798
## 8.431105e-05 1.231421e-04 1.334256e-04 3.172025e-05 5.740208e-05
## 5930 1955 7073 6380 6962
## 2.089184e-06 3.638189e-06 6.298201e-05 6.500038e-06 2.293824e-05
## 7944 8278 8345 8183 7363
## 1.818942e-06 4.563380e-06 2.335251e-06 9.422861e-04 2.008903e-06
## 7917 5810 7879 745 2914
## 2.878423e-04 7.966876e-06 3.550578e-04 1.329540e-04 2.602070e-05
## 7655 2021 5547 2319 6318
## 3.562680e-04 2.770685e-05 5.682239e-05 6.841473e-05 8.442315e-05
## 7703 4312 7822 3484 5466
## 9.865922e-05 3.345900e-06 7.167292e-05 8.565359e-06 2.481835e-06
## 4360 6289 8101 4624 9838
## 2.636390e-04 1.165505e-04 1.304615e-04 6.029694e-05 5.102386e-05
## 4600 1126 3247 4791 4698
## 2.416956e-06 1.326629e-03 8.334049e-04 9.608398e-07 2.541166e-05
## 5440 6019 9643 688 196
## 5.777462e-06 6.396281e-04 6.446044e-06 1.630902e-04 1.406941e-03
## 835 10 2222 8454 8033
## 2.487704e-05 2.006650e-06 4.078681e-04 2.488747e-04 1.039660e-06
## 129 2966 259 7356 6714
## 6.242550e-04 9.225044e-05 1.859286e-03 1.066218e-03 5.102237e-04
## 8856 3509 9677 8171 6153
## 4.702798e-07 2.951370e-05 6.971584e-05 5.636898e-04 4.903250e-06
## 2290 3347 9228 7341 4625
## 3.870976e-04 5.105819e-04 1.614541e-04 1.528629e-04 1.674141e-04
## 5760 765 4844 9169 7967
## 4.822956e-05 8.241654e-06 3.080724e-04 1.685213e-04 4.698122e-05
## 3802 2744 8790 4449 7471
## 5.231642e-04 8.452337e-06 1.063112e-04 5.965699e-04 7.751205e-06
## 4398 1028 7658 2108 7199
## 1.754092e-05 1.442684e-04 3.478535e-08 7.624343e-04 5.242703e-04
## 4535 3636 2662 8651 1831
## 7.554584e-05 2.486982e-04 1.283058e-04 3.601443e-05 2.243987e-04
## 1322 282 4912 9405 6014
## 2.519243e-04 3.998436e-05 1.567635e-04 3.673233e-04 5.248442e-06
## 6792 8299 9298 6200 6580
## 3.659364e-04 1.815077e-05 5.674000e-05 1.537067e-04 2.006286e-04
## 8681 5984 1900 9975 4465
## 5.331610e-06 6.873292e-05 6.910462e-04 7.031719e-04 5.126389e-05
## 4127 8822 9888 8509 7593
## 1.965003e-04 6.783464e-04 1.506758e-04 1.791856e-05 1.699305e-04
## 4831 8111 3419 4984 9289
## 1.282543e-04 1.171441e-03 2.875664e-06 4.608770e-05 3.515208e-05
## 4208 3043 7886 322 4796
## 1.186171e-06 2.221900e-05 1.110901e-05 1.399213e-04 8.506079e-06
## 5775 7419 1355 3672 2703
## 2.185771e-04 2.406025e-04 3.127506e-05 2.503055e-05 6.432783e-06
## 7352 1601 6848 8910 1189
## 8.617767e-05 1.699430e-04 4.029479e-04 2.034950e-04 1.084760e-04
## 1905 7697 4928 7842 6608
## 2.682695e-07 1.750183e-04 9.337277e-06 4.364780e-07 3.221775e-05
## 8187 3089 630 5887 9721
## 2.972295e-05 7.029538e-05 5.936971e-05 9.410629e-06 1.925206e-04
## 5037 2791 4675 4648 7174
## 7.188670e-05 2.321512e-06 5.264992e-05 5.126552e-06 7.026943e-05
## 8708 5358 5844 3388 9977
## 1.645591e-04 2.665990e-04 7.245512e-04 3.000126e-04 3.862367e-05
## 8949 2013 5115 9149 108
## 1.125104e-04 2.041417e-04 2.197909e-06 6.929497e-04 2.856892e-05
## 6084 3678 5061 4557 182
## 3.500116e-07 4.681756e-04 2.040463e-04 1.905913e-04 1.007258e-03
## 5894 9665 1176 1757 6505
## 8.942918e-06 7.325222e-07 8.335190e-05 1.328030e-05 1.049502e-04
## 1967 6481 9240 8530 2103
## 6.022603e-05 6.132847e-04 6.370041e-05 1.402093e-04 4.573974e-05
## 209 1036 7580 6888 3279
## 1.603360e-04 1.260793e-05 3.117679e-04 1.131970e-04 3.273079e-05
## 9440 6355 5008 589 4147
## 4.493319e-06 2.979309e-04 4.125675e-05 1.762809e-04 5.996347e-04
## 7991 3098 6789 4652 1627
## 1.551841e-04 4.257132e-06 6.047336e-04 4.412538e-04 9.873387e-05
## 294 6625 5020 8797 2917
## 5.308685e-05 3.507472e-06 1.779629e-04 2.053442e-07 2.636949e-04
## 146 954 508 5247 6066
## 1.207800e-05 2.957279e-04 8.963978e-04 1.140449e-05 1.072859e-04
## 8639 2383 439 7217 7398
## 1.188080e-04 4.840721e-04 1.178482e-04 4.623371e-05 2.705156e-04
## 9191 8559 9476 7866 2834
## 3.377436e-04 1.349160e-05 1.769234e-05 2.621443e-05 9.043845e-06
## 3993 9907 2275 5445 9876
## 3.642637e-05 1.207994e-05 2.686342e-05 6.608354e-05 3.454882e-05
## 2517 690 364 5638 5471
## 2.149132e-05 7.985492e-06 2.620384e-05 1.517165e-05 3.272097e-04
## 8242 3934 6339 9362 9924
## 8.174705e-05 1.593374e-06 9.620233e-05 3.086962e-06 2.037918e-04
## 2523 7161 659 5907 243
## 1.085222e-04 7.969535e-05 5.058651e-05 1.873481e-04 9.701770e-04
## 913 8382 6150 8282 4908
## 2.286603e-04 2.097787e-04 2.428070e-07 5.660889e-05 1.359323e-08
## 9960 4692 4929 1492 5723
## 9.670023e-05 1.863819e-06 1.792448e-04 5.881082e-05 4.159081e-04
## 3183 8128 2341 7291 9769
## 8.976506e-05 3.749131e-04 3.389995e-04 2.316518e-04 9.234279e-05
## 7198 4125 9868 5573 1830
## 5.978689e-06 1.536184e-04 2.214326e-05 1.756453e-04 1.248398e-05
## 4694 435 4561 6864 5568
## 1.664691e-04 8.335816e-04 2.197727e-04 2.075175e-04 1.113643e-04
## 1061 6981 1358 1286 2693
## 2.466017e-04 4.627894e-08 6.801133e-05 5.568373e-05 1.906279e-04
## 1276 4015 3204 9103 3583
## 6.980005e-06 4.553034e-05 6.651455e-06 1.387883e-04 1.649083e-05
## 5819 9125 3617 3138 773
## 3.288600e-04 6.933414e-07 1.385943e-04 1.286517e-06 2.400354e-04
## 7223 991 3478 5649 7505
## 3.496878e-04 5.223709e-05 1.111087e-04 3.026810e-04 4.239211e-04
## 1723 5305 1564 9927 5572
## 1.471040e-05 1.337093e-04 1.783142e-04 7.088026e-05 2.747270e-04
## 3749 3255 4890 6364 1648
## 1.998080e-04 5.056074e-04 8.627866e-06 1.235306e-06 7.990304e-04
## 8766 1511 3200 5577 8029
## 4.588391e-04 1.737644e-04 6.148123e-06 1.887860e-05 1.586191e-04
## 7712 440 8009 4001 7041
## 9.343864e-05 1.009367e-04 4.718403e-05 1.009575e-04 2.114253e-05
## 7618 7656 3697 5484 9745
## 4.504589e-06 8.842432e-05 4.334421e-04 1.547063e-04 3.375731e-05
## 1734 7624 1961 3004 6507
## 3.470570e-04 2.663508e-05 2.906964e-04 6.048203e-05 9.690675e-04
## 5375 800 8368 644 2348
## 1.062047e-04 3.582289e-04 4.067337e-04 3.977985e-05 1.168129e-04
## 9972 6861 4681 1863 2086
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## 9.476239e-05 4.231144e-06 5.565483e-04 1.100881e-04 1.143487e-04
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## 3.866247e-04 1.487431e-04 1.645083e-04 3.574779e-07 8.333554e-04
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## 3.839608e-05 4.348862e-05 4.299466e-05 3.946106e-05 1.278014e-05
## 9761 2223 9930 5362 2298
## 1.947128e-04 4.040290e-07 1.629947e-06 1.602598e-04 2.320109e-04
## 9641 3433 6307 9531 7007
## 1.998511e-04 1.545080e-06 5.658895e-04 2.414451e-05 5.210002e-05
## 7755 8517 9674 9763 9691
## 1.491157e-06 3.387513e-04 4.450761e-07 5.848743e-05 6.834015e-07
## 2859 3562 546 7319 5599
## 2.503341e-04 8.317776e-06 2.247084e-04 1.642443e-05 7.368142e-06
## 5994 9650 9484 9006 5583
## 9.595546e-06 1.535097e-04 4.098990e-04 1.537707e-04 7.198085e-04
## 5931 7340 7972 3080 302
## 4.597173e-04 1.167595e-04 4.216894e-05 1.473966e-05 4.448939e-05
## 7742 5333 4411 8597 6173
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## 7035 5514 1314 5823 1675
## 5.732904e-05 1.455149e-05 3.693056e-07 2.111173e-05 2.392460e-05
## 2293 1234 8750 4641 1292
## 1.245910e-03 2.045664e-04 7.224351e-04 7.635387e-06 2.470610e-04
## 9085 125 9580 2806 6057
## 7.486174e-09 3.203165e-06 1.486094e-05 8.257381e-05 7.970345e-06
## 3270 5062 7274 409 250
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## 3698 989 2609 4626 1070
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## 1582 941 3339 9098 7720
## 4.343442e-04 1.591653e-05 2.120584e-06 4.906063e-05 9.952803e-05
## 9422 5066 8233 636 8484
## 1.029355e-04 2.563518e-05 8.579758e-05 2.101736e-04 2.489134e-04
## 7310 4612 4750 9587 3537
## 8.698713e-05 2.045442e-05 2.451716e-04 9.763050e-05 1.537870e-05
## 5330 7935 8710 4816 4372
## 3.903940e-04 5.463940e-04 5.076097e-04 5.109419e-04 5.735775e-04
## 5588 6631 9953 5985 8333
## 2.479157e-05 8.463565e-05 4.440027e-06 7.428134e-05 2.304564e-04
## 2905 5643 6069 782 7615
## 4.639953e-05 2.677327e-05 3.220272e-04 4.358252e-05 1.111638e-04
## 6800 1125 6849 1827 5992
## 3.584770e-04 1.164319e-06 2.016671e-04 1.179538e-12 4.200445e-04
## 7349 9489 4952 1058 3601
## 8.508068e-05 5.170988e-05 1.433716e-05 6.580913e-05 1.993369e-04
## 3710 6194 1604 5351 5009
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## 7220 2041 3984 2862 4921
## 5.809751e-05 7.431535e-06 1.351312e-06 1.194041e-05 1.518356e-05
## 2780 4986 424 159 9344
## 1.710642e-04 3.708615e-04 4.828867e-04 3.278921e-04 3.752829e-05
## 9225 574 4217 5134 1600
## 1.432526e-04 4.724374e-05 1.325790e-05 4.862275e-05 4.500705e-05
## 1493 4280 9281 5680 4340
## 2.695527e-04 3.522256e-04 2.814917e-05 2.993413e-04 8.481774e-05
## 1815 695 946 4425 6773
## 1.402661e-05 1.082598e-04 2.358198e-05 1.027689e-04 3.343075e-04
## 9899 1993 459 7484 9909
## 2.419661e-04 4.442783e-05 1.618811e-07 5.839624e-05 1.039352e-06
## 8945 2171 9923 5492 9623
## 3.138093e-04 2.897782e-05 7.829758e-05 6.831114e-05 8.895644e-05
## 8200 5597 4931 9388 7026
## 5.260798e-04 2.170679e-04 1.788376e-04 7.178136e-05 3.152219e-04
## 8298 5880 7267 8422 6044
## 6.000215e-04 9.717325e-05 2.637009e-04 4.999703e-05 4.878751e-07
## 3087 8273 5223 1971 7603
## 2.066509e-04 7.217793e-04 7.868996e-04 4.467801e-06 1.657526e-04
## 12 5123 8537 3603 6300
## 6.364457e-08 4.899189e-05 2.662753e-04 1.802703e-06 2.360132e-05
## 1100 8579 3282 6715 6532
## 3.561865e-04 3.834450e-05 1.994485e-05 2.489115e-06 1.284125e-04
## 8538 1581 7949 4446 1079
## 9.771189e-04 5.239098e-05 8.620097e-05 2.079304e-04 7.805781e-05
## 8211 7675 2920 1743 5778
## 1.770598e-05 1.339161e-04 5.961810e-06 4.279664e-07 9.802510e-04
## 1512 3112 7296 9465 2515
## 9.508998e-07 5.042146e-05 6.388071e-05 1.414848e-06 1.953412e-05
## 6509 791 4385 6401 9629
## 5.847024e-04 2.067479e-04 1.100846e-05 8.071572e-05 7.143066e-06
## 2789 7790 5084 3021 5703
## 6.223539e-05 2.114075e-04 9.318179e-05 7.523140e-05 1.036750e-04
## 5590 1687 9038 2596 6657
## 6.679233e-04 6.051267e-05 3.320158e-04 1.643464e-05 1.397787e-05
## 7890 3299 3766 7094 1231
## 1.427330e-04 3.024944e-07 1.692484e-06 7.008971e-04 9.446012e-06
## 9542 6585 9257 4224 1280
## 5.577863e-05 2.910049e-04 1.035097e-04 1.264405e-04 3.029206e-04
## 1275 2745 1929 7753 2
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## 383 8867 9474 2696 3908
## 1.474936e-05 8.365331e-04 1.723632e-04 2.495374e-04 2.088827e-04
## 6552 8353 3681 4970 3238
## 1.438119e-06 5.009618e-04 4.486100e-04 4.313640e-04 7.370590e-04
## 1130 29 1558 8534 9891
## 2.426210e-08 8.519559e-05 3.255524e-05 1.555579e-06 1.572755e-05
## 2099 590 4434 5136 7563
## 2.844314e-04 3.031131e-04 3.433553e-04 9.563911e-05 1.169884e-05
## 7916 9503 6540 3468 738
## 7.744446e-04 3.584583e-05 2.247155e-05 2.426198e-05 1.413465e-04
## 4990 1271 820 4955 3872
## 1.804764e-05 8.666445e-05 1.668510e-07 2.803012e-04 7.560825e-05
## 7569 1718 5449 4693 7690
## 1.309887e-05 2.174247e-04 4.386166e-05 6.941276e-04 3.570873e-04
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## 2506 7641 2732 5229 4866
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## 9533 3068 3303 199 9142
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## 9411 8289 3463 3355 1426
## 2.227596e-04 3.923125e-04 2.475058e-05 2.018236e-06 6.201981e-04
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## 150 895 8153 3053 3795
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## 445 6302 5762 5969 7787
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## 4782 9818 5881 920 8621
## 2.154224e-04 8.503898e-06 1.792796e-05 1.322754e-04 2.791230e-05
## 6504 5221 7609 1522 9423
## 1.675422e-03 1.500237e-05 3.855609e-04 5.035378e-05 2.791214e-04
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## 2.037608e-07 2.444332e-05 2.647742e-06 6.418073e-04 1.719316e-04
## 1190 7222 4231 2321 638
## 1.242260e-04 5.310472e-05 6.443274e-06 8.651313e-04 3.971791e-04
## 2800 2320 4086 4950 4196
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## 1526 4071 3226 7648 6448
## 2.268074e-04 4.360641e-06 1.265423e-05 9.902708e-06 3.113916e-04
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## 6.622160e-06 1.588849e-04 3.194528e-04 7.172476e-04 4.028660e-05
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## 5644 6067 9090 6260 9472
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## 276 8613 9035 4774 9987
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## 153 266 1686 4376 3451
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## 3595 693 235 7051 1084
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## 3.953357e-04 6.135265e-04 1.528712e-04 1.045834e-05 9.668472e-06
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## 2.046162e-04 3.133707e-05 4.342571e-05 6.630331e-05 2.229470e-04
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## 2.372838e-05 3.027220e-04 1.170837e-05 3.075925e-04 2.493586e-07
## 4587 1421 2401 2185 2440
## 5.764964e-06 2.328975e-06 2.167415e-04 5.529502e-04 6.617989e-04
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## 1.651682e-04 4.730381e-05 9.324585e-07 9.170613e-06 5.762803e-05
## 5380 6325 803 5258 957
## 1.277631e-04 6.491296e-04 3.230613e-05 2.823894e-05 2.323334e-04
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## 1.772955e-07 3.033054e-05 2.968071e-06 9.300509e-05 5.146038e-06
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## 3.427376e-04 6.195725e-04 1.501946e-04 2.290475e-04 1.301375e-05
## 6905 1166 7061 4933 7305
## 4.053362e-05 1.661048e-04 1.216290e-04 1.177636e-05 4.614350e-07
## 5606 6929 9148 3711 6107
## 1.692453e-06 9.297761e-04 2.825005e-06 1.586791e-05 5.955482e-07
## 9446 7367 6092 2991 8953
## 6.033128e-05 2.616183e-05 4.903449e-06 1.476032e-05 2.709947e-04
## 5756 1116 4076 4541 931
## 3.095788e-05 7.729045e-05 6.402531e-05 5.475357e-04 1.307735e-05
## 3292 2066 5619 6698 5516
## 6.185064e-04 2.237554e-06 1.820078e-04 2.363543e-04 1.712979e-04
## 1250 3365 6763 1949 5148
## 2.867325e-04 5.691161e-05 3.552429e-05 4.909900e-09 1.865031e-05
## 3495 663 3581 7520 9259
## 1.650176e-04 1.469067e-06 5.183082e-07 8.829396e-06 8.328805e-04
## 5086 8587 7469 4003 6753
## 1.946722e-04 2.115628e-04 5.744251e-05 2.241873e-06 2.413087e-04
## 4630 5007 9976 5744 8558
## 1.413250e-04 1.024536e-03 1.138863e-04 2.928182e-07 1.519537e-04
## 5005 5584 2867 5519 9070
## 4.061692e-05 9.256413e-05 2.649680e-04 4.625117e-05 1.758638e-04
## 4392 2975 3435 4476 8164
## 1.683896e-05 1.934470e-04 9.007808e-09 3.074954e-06 9.628019e-05
## 608 7626 2492 1960 1986
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## 6963 1258 2928 8155 1237
## 1.790610e-04 1.850666e-04 3.846769e-04 4.167498e-05 8.189842e-07
## 5622 5874 553 3742 7987
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## 8627 7413 8049 1404 4666
## 8.533543e-08 2.090061e-04 3.595624e-07 3.472727e-05 2.777530e-06
## 8316 5858 5054 4537 6157
## 1.006787e-05 9.513562e-05 1.003998e-05 1.600029e-05 2.747088e-05
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## 8.644625e-04 4.997465e-05 5.260081e-05 1.523443e-04 2.513084e-05
## 9320 3399 4284 660 4070
## 5.670089e-05 1.304482e-04 2.780586e-05 3.144297e-04 7.303194e-05
## 2396 6638 7314 5350 7841
## 2.986402e-04 3.285148e-04 1.504235e-04 1.100475e-05 1.968418e-03
## 6863 1555 1909 2003 8531
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## 2477 9037 872 1387 3613
## 5.462131e-04 6.264475e-04 3.397835e-04 1.584677e-03 1.240443e-04
## 8195 5759 1677 5878 2241
## 8.236532e-07 2.185449e-05 3.764111e-04 3.130678e-04 6.599529e-05
## 6354 1494 7403 2010 4872
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## 4804 4598 7953 1694 7247
## 7.806405e-06 1.193062e-04 2.660226e-06 1.300268e-04 6.358606e-04
## 1490 9860 3594 3905 6313
## 5.485302e-04 8.201843e-05 1.014364e-05 3.167728e-04 2.047964e-05
## 9302 9771 635 9559 1127
## 2.447330e-06 1.387385e-05 5.512292e-05 1.365128e-04 1.168402e-05
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## 1735 8021 8012 7925 141
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## 9110 1132 9801 2713 8999
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## 3.002896e-04 8.505702e-06 1.017202e-04 1.203905e-04 2.753648e-06
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## 5.481957e-05 1.287865e-03 1.752086e-04 1.414260e-04 2.266147e-05
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## 2974 8753 4674 1748 1950
## 2.951069e-04 5.627834e-08 7.708257e-05 1.332879e-07 2.535553e-04
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## 4327 321 5138 246 1541
## 9.028261e-05 8.424871e-05 6.202650e-04 5.274925e-08 1.437757e-04
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## 1068 9443 9078 3762 8780
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## 7258 7058 4862 8775 1854
## 6.419056e-05 2.199504e-04 2.462100e-06 2.483007e-04 2.526031e-04
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## 9590 8731 7638 1180 9956
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## 2204 7401 3501 465 1587
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## 3 3210 3626 4910 4211
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## 6254 6933 3944 3061 6988
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## 2240 1970 4035 7213 3528
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## 1.350756e-04 3.042988e-05 6.932742e-06 4.236819e-04 6.512953e-07
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## 7.669508e-05 6.451180e-05 7.117398e-06 6.791517e-07 1.483246e-04
## 2455 5800 8083 3673 8892
## 2.708355e-04 5.840221e-06 6.809106e-06 2.958431e-04 1.275635e-05
## 1228 2912 4100 7882 7081
## 9.298349e-06 3.649444e-06 2.441741e-04 1.726120e-05 3.670428e-06
## 4869 6709 1619 2203 1794
## 1.845094e-04 1.483524e-05 2.628350e-04 1.360200e-04 3.477749e-04
## 2137 1420 1267 8001 7667
## 4.617259e-08 5.683581e-07 2.747608e-06 2.474193e-06 8.173147e-05
## 8286 5190 3453 9306 947
## 4.254311e-04 6.755357e-05 4.196374e-04 3.390999e-04 5.218137e-04
## 8997 7397 80 7104 2248
## 2.089920e-04 3.660431e-04 1.934106e-04 1.213041e-04 8.494705e-05
## 8064 8024 1207 9709 1942
## 8.660960e-04 2.571640e-08 2.336653e-07 5.297631e-05 4.330808e-06
## 667 650 5628 2603 466
## 1.287251e-06 9.765261e-05 4.957058e-07 5.243893e-04 1.212175e-04
## 7339 5111 9283 8716 7846
## 5.741105e-04 8.066179e-06 4.515496e-04 4.746990e-05 4.064149e-05
## 4150 8975 888 5865 7889
## 7.511667e-05 5.855777e-05 2.520508e-04 3.962251e-04 1.346766e-06
## 411 1272 102 2205 3178
## 2.022543e-04 3.569097e-05 7.231259e-05 3.733999e-05 4.946226e-06
## 5531 6238 2645 5366 7865
## 8.453713e-05 8.717015e-05 2.536792e-04 5.154076e-05 5.368938e-05
## 4149 4167 1849 3894 2031
## 7.264251e-04 3.855277e-04 2.437133e-04 1.566141e-04 6.370113e-05
## 1248 380 7370 3856 887
## 9.050163e-06 1.177450e-11 3.111949e-04 6.682181e-05 4.026512e-05
## 3833 3818 3257 8428 1766
## 3.013702e-05 5.731034e-04 6.784833e-04 2.647537e-05 3.296090e-04
## 1571 9749 3652 1136 9490
## 2.378553e-04 6.005547e-06 1.137690e-04 1.823680e-04 6.545222e-06
## 3283 6125 6910 4060 8500
## 2.523709e-05 7.705146e-05 1.026526e-04 9.294447e-05 3.455005e-06
## 1386 8747 3219 5266 7502
## 4.523398e-06 3.409560e-05 4.440085e-05 7.340829e-05 5.812944e-06
## 9759 7583 1514 3937 4669
## 4.837046e-04 1.853994e-04 6.755876e-04 6.668568e-06 1.011028e-04
## 1341 1580 6695 6078 9781
## 1.171891e-03 7.330816e-06 2.168443e-05 3.024198e-05 5.589204e-06
## 4634 5502 1081 2004 7098
## 6.983900e-07 8.242906e-05 6.542840e-04 5.276436e-05 8.172785e-05
## 7632 845 7950 1037 5053
## 3.024547e-04 1.189548e-04 6.297139e-06 1.036706e-05 1.947540e-04
## 2444 7880 2350 8040 9357
## 2.624244e-04 3.176073e-06 2.934209e-05 1.881361e-06 5.113011e-05
## 6423 1221 3705 7783 4610
## 4.148088e-07 1.729378e-04 1.249993e-04 2.208795e-05 1.684972e-04
## 5249 759 9986 8264 771
## 1.635361e-04 1.430960e-06 1.446594e-04 8.418217e-05 1.743807e-04
## 1312 8402 91 4907 1991
## 2.645367e-05 5.404610e-04 2.508435e-05 2.723357e-04 1.493583e-06
## 7461 3725 1075 9642 2436
## 6.805911e-05 4.080137e-04 3.979638e-06 9.951396e-04 8.261854e-05
## 9066 7748 7996 4266 9582
## 6.813257e-08 1.607805e-04 8.969599e-04 1.741989e-04 6.785477e-05
## 2621 6958 5175 8641 1937
## 5.215066e-04 5.592918e-05 4.034831e-05 2.029856e-05 3.621577e-04
## 9500 4566 9814 7300 2468
## 7.485105e-04 1.654334e-04 3.581210e-06 1.385373e-05 2.391402e-04
## 7777 5837 5273 5312 9779
## 2.640607e-04 7.769412e-05 3.561295e-04 4.160725e-05 1.315512e-05
## 3904 9145 7751 4937 7878
## 7.530796e-05 4.743312e-04 1.296900e-05 7.553952e-05 1.853888e-05
## 5354 175 5415 2363 6308
## 6.896157e-05 5.910428e-05 2.776314e-04 8.776074e-05 7.216138e-06
## 1034 9470 2653 2540 9158
## 5.147280e-04 6.453321e-05 2.599632e-05 7.051593e-07 3.424342e-05
## 6188 72 6967 8863 1394
## 1.860674e-04 3.772942e-05 5.715958e-04 1.242746e-05 5.358664e-04
## 1808 649 4815 388 2850
## 1.645371e-05 1.639692e-05 4.107642e-05 1.273566e-04 5.691765e-05
## 1681 4113 795 7758 6174
## 1.444432e-06 2.986990e-05 1.353903e-04 2.166830e-04 1.109336e-04
## 9458 6828 7235 3788 8884
## 2.011456e-04 1.536160e-05 1.423890e-04 9.760003e-04 6.149161e-05
## 7962 238 1385 5467 7078
## 3.968500e-05 2.404706e-04 1.914428e-05 5.946246e-05 1.207409e-06
## 7453 1080 5922 3268 6391
## 5.436144e-05 7.427793e-04 4.111011e-05 1.562896e-04 7.009829e-05
## 9213 7200 3903 8734 9653
## 8.310857e-05 2.760185e-05 1.496136e-04 1.781015e-04 1.017904e-04
## 6652 5329 3540 2430 6776
## 2.806105e-04 1.639766e-04 1.590391e-06 6.889652e-05 9.186520e-05
## 6037 6117 9967 778 6759
## 3.441510e-04 1.175392e-05 5.867105e-05 5.280651e-04 1.012920e-04
## 9864 8257 7788 4635 3500
## 8.451090e-05 1.750061e-04 1.448276e-04 1.685204e-04 4.043497e-08
## 6704 8112 9248 5973 9043
## 5.353576e-04 3.920867e-04 5.415234e-06 2.486286e-07 1.146954e-03
## 5651 8878 8914 6413 4810
## 1.485347e-04 1.912879e-04 9.932280e-05 7.147783e-06 7.904226e-06
## 5051 6217 3838 5306 226
## 1.644757e-04 5.234622e-04 3.504752e-04 3.242519e-05 1.958141e-05
## 8745 8172 3567 4394 9921
## 1.202571e-04 5.088088e-05 9.476039e-05 1.237428e-05 2.216683e-05
## 9219 4787 9202 2409 8122
## 1.484486e-05 2.286885e-04 1.281051e-05 1.049165e-04 4.625533e-05
## 1308 2989 21 4057 2875
## 6.267298e-04 2.285299e-04 5.413528e-06 2.557916e-05 8.365534e-06
## 9354 2233 3179 651 9088
## 9.308384e-05 1.918215e-04 4.225406e-05 2.330507e-04 9.882734e-05
## 2365 6935 3320 8528 4893
## 1.080980e-04 3.699567e-05 4.274420e-05 4.934586e-05 2.837957e-05
## 4838 7001 6731 3209 3160
## 2.443624e-04 1.168973e-05 2.046401e-04 9.587072e-05 3.380618e-05
## 974 2651 2638 8740 948
## 6.969931e-05 7.366009e-05 1.512902e-04 8.782370e-04 2.046520e-04
## 9562 8767 8584 8774 6996
## 4.136646e-04 5.176741e-08 4.236101e-05 8.922978e-04 3.818580e-05
## 8193 4325 9716 4286 5225
## 2.262478e-05 6.838527e-04 6.700645e-06 2.904237e-05 8.436294e-06
## 7614 7256 5228 3031 2498
## 2.073822e-05 3.928575e-04 5.505055e-05 2.159166e-05 3.378491e-05
## 60 5283 5079 3780 2965
## 4.548989e-04 3.910908e-05 7.228705e-04 2.965747e-04 4.975240e-05
## 9241 4136 2192 2195 5770
## 1.000584e-03 4.227585e-08 1.178328e-05 1.386989e-04 2.111990e-04
## 8847 2533 5940 5052 9654
## 2.843764e-04 7.527551e-05 1.390457e-04 9.496969e-05 1.812361e-06
## 9176 2335 8032 9023 4260
## 6.226967e-05 3.894058e-04 8.648954e-05 2.496518e-04 2.446027e-06
## 1692 5674 1470 1755 5381
## 7.064291e-05 1.303662e-03 1.974831e-04 4.585687e-04 2.029290e-04
## 5835 8893 304 5141 2168
## 9.007912e-05 2.396290e-13 1.324385e-05 1.181350e-04 1.198594e-04
## 7303 2364 8494 8044 4077
## 5.148541e-04 1.318019e-05 7.035536e-05 4.546696e-05 5.132720e-05
## 9083 4424 5804 3472 5596
## 1.669473e-04 5.151871e-05 8.605569e-04 7.808157e-04 9.061227e-07
## 8811 6252 1745 2770 4963
## 3.100592e-05 9.720278e-05 4.348003e-04 5.769075e-05 1.161070e-05
## 4171 9822 8203 6771 8593
## 2.422341e-04 9.475732e-04 1.828894e-04 6.593561e-07 4.227674e-04
## 447 892 8782 9410 4913
## 2.039456e-07 1.278186e-04 1.191977e-04 8.223967e-05 9.262799e-05
## 158 6343 9162 3379 691
## 1.011188e-03 6.722369e-05 5.243361e-05 1.543551e-05 7.235172e-05
## 5423 4851 18 5417 2419
## 3.271734e-05 2.272298e-05 5.957191e-05 4.258209e-05 1.368377e-05
## 1861 5428 392 8323 1927
## 6.843857e-05 6.562292e-05 1.011070e-04 1.173037e-04 7.381768e-06
## 960 4298 1019 5303 4731
## 3.671838e-09 4.863600e-04 6.411786e-05 4.801069e-04 2.754642e-06
## 6183 4317 2276 3069 4877
## 4.558444e-04 3.822751e-05 9.862776e-06 3.229695e-05 2.570522e-04
## 4889 9737 3397 404 7526
## 3.072466e-05 2.620537e-05 2.539592e-05 3.331565e-05 2.215546e-04
## 903 4219 3408 8574 8713
## 1.368284e-04 4.111716e-05 1.617837e-05 3.570103e-05 5.532626e-04
## 96 1550 3147 5103 6322
## 2.250105e-06 2.380786e-04 4.309233e-04 6.915419e-05 4.474694e-04
## 2737 2148 4835 137 4949
## 9.394471e-06 7.875519e-05 6.042210e-05 8.629932e-05 6.203529e-05
## 7360 4287 4247 9135 6566
## 3.092779e-04 3.059630e-05 5.961196e-04 1.468812e-04 2.129407e-04
## 5387 2413 8568 9917 4302
## 6.474978e-05 8.657302e-05 1.704706e-04 7.541477e-06 3.177651e-05
## 8712 5773 6264 5636 6298
## 8.777729e-05 1.914247e-04 4.922436e-04 1.240389e-04 2.364693e-04
## 4308 8615 4373 9568 7493
## 7.618822e-06 5.266481e-04 1.550574e-04 1.239336e-05 2.541520e-04
## 2162 3923 9845 8037 6130
## 1.152340e-04 3.330661e-04 1.868244e-05 6.923680e-04 2.523874e-05
## 2411 3758 1186 3114 7241
## 5.187037e-05 1.272190e-04 3.973253e-05 5.901277e-05 1.800712e-05
## 3465 3369 5335 5477 1724
## 3.738000e-05 6.439452e-04 1.335629e-05 1.196332e-05 4.748754e-05
## 1886 1251 472 2860 9356
## 1.480599e-06 3.522445e-05 6.631612e-06 1.965444e-04 3.467822e-06
## 4273 228 3941 849 3884
## 1.189013e-05 1.697184e-05 1.555411e-04 2.885329e-04 8.037266e-05
## 2157 3187 1047 8436 7605
## 1.403868e-07 3.002823e-04 4.453531e-04 3.902740e-07 3.448415e-06
## 5222 1491 942 3840 580
## 2.603597e-04 1.348671e-03 1.613798e-04 1.026026e-04 1.461650e-04
## 4177 334 7812 1796 7424
## 2.524242e-04 5.451409e-05 6.956652e-05 1.202739e-05 1.912548e-04
## 7293 8812 7197 4063 1959
## 3.668042e-04 2.538180e-04 1.211871e-03 2.166887e-05 8.110826e-06
## 1772 7353 5377 4932 7732
## 4.100383e-04 2.686504e-04 2.420549e-06 6.468336e-05 1.955544e-06
## 1652 9120 6425 5260 7867
## 1.185609e-07 4.210658e-06 2.867313e-04 4.926068e-04 1.443059e-04
## 6836 4319 5640 4516 1212
## 4.857903e-05 7.741834e-05 4.349844e-05 1.532510e-04 1.042341e-04
## 4653 4958 7010 9698 5164
## 4.621936e-08 5.854961e-05 9.125374e-07 6.727372e-04 3.246093e-06
## 5401 7160 1172 5605 4209
## 4.078865e-04 2.638089e-04 7.742168e-04 2.346997e-06 5.222503e-04
## 1875 7436 271 6028 9571
## 1.526970e-04 1.412623e-06 2.657622e-05 4.999296e-04 3.695739e-04
## 5359 5834 3659 5398 5069
## 9.130007e-04 1.019912e-04 1.975999e-05 2.074855e-04 1.159362e-04
## 714 8785 1233 4361 1837
## 3.309771e-06 1.350620e-04 9.897516e-06 3.204400e-06 5.768893e-04
## 6620 4388 8931 6599 1693
## 6.609085e-05 1.355299e-04 8.516770e-04 1.397237e-06 4.827793e-05
## 3074 3927 7034 1817 4462
## 3.607493e-05 4.384444e-05 7.859705e-06 2.506111e-05 7.221795e-08
## 8698 6782 7460 3782 315
## 4.576051e-04 7.179281e-04 5.355851e-07 3.905522e-06 8.649699e-08
## 8169
## 6.726280e-07Variable Selection
http://www.stat.columbia.edu/~martin/W2024/R10.pdf
Forward Selection (w/ full train)
Train
if (algo.forward == TRUE){
t1 = Sys.time()
model.forward = step(model.null, scope=list(lower=model.null, upper=model.full), direction="forward", trace = 0)
print(summary(model.forward))
saveRDS(model.forward,file = "model_forward.rds")
t2 = Sys.time()
print (paste("Time taken for Forward Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.forward, data.train)
}##
## Call:
## lm(formula = y3 ~ sqrt.x18 + x7 + stat98 + stat110 + x9 + x4 +
## x16 + x17 + x10 + x8 + stat14 + stat41 + x21 + x11 + stat4 +
## stat26 + stat54 + stat187 + stat48 + stat92 + stat151 + stat172 +
## stat100 + stat23 + stat43 + stat214 + stat94 + stat46 + stat37 +
## stat13 + stat87 + x14 + stat19 + stat35 + stat45 + stat158 +
## stat156 + stat199 + stat33 + stat70 + stat207 + stat204 +
## stat25 + stat22 + stat144 + stat38 + stat146 + stat3 + stat60 +
## x12 + stat89 + stat10 + stat175 + stat141 + stat161, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.908 -6.131 -1.780 4.446 69.908
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.041e+01 2.393e+00 37.783 < 2e-16 ***
## sqrt.x18 7.294e+00 2.669e-01 27.330 < 2e-16 ***
## x7 3.162e+00 1.809e-01 17.480 < 2e-16 ***
## stat98 1.013e+00 6.912e-02 14.649 < 2e-16 ***
## stat110 -9.391e-01 7.033e-02 -13.351 < 2e-16 ***
## x9 9.663e-01 9.422e-02 10.256 < 2e-16 ***
## x4 -1.337e-02 2.561e-03 -5.223 1.82e-07 ***
## x16 2.918e-01 6.095e-02 4.788 1.73e-06 ***
## x17 3.917e-01 9.239e-02 4.239 2.28e-05 ***
## x10 3.212e-01 8.731e-02 3.679 0.000236 ***
## x8 1.333e-01 4.209e-02 3.166 0.001551 **
## stat14 -2.198e-01 6.954e-02 -3.160 0.001585 **
## stat41 -1.813e-01 6.994e-02 -2.592 0.009572 **
## x21 3.383e-02 1.199e-02 2.822 0.004793 **
## x11 5.408e+07 2.092e+07 2.585 0.009754 **
## stat4 -1.955e-01 7.082e-02 -2.761 0.005781 **
## stat26 -1.697e-01 7.026e-02 -2.416 0.015728 *
## stat54 -1.698e-01 7.079e-02 -2.399 0.016468 *
## stat187 -1.670e-01 7.026e-02 -2.377 0.017476 *
## stat48 1.446e-01 7.101e-02 2.037 0.041737 *
## stat92 -1.339e-01 7.059e-02 -1.897 0.057912 .
## stat151 -1.410e-01 7.093e-02 -1.988 0.046860 *
## stat172 1.329e-01 7.037e-02 1.888 0.059013 .
## stat100 1.595e-01 7.040e-02 2.265 0.023538 *
## stat23 1.475e-01 6.966e-02 2.118 0.034247 *
## stat43 -1.483e-01 7.055e-02 -2.102 0.035618 *
## stat214 -1.449e-01 7.018e-02 -2.065 0.038991 *
## stat94 -1.458e-01 7.046e-02 -2.069 0.038628 *
## stat46 1.353e-01 7.050e-02 1.919 0.055011 .
## stat37 -1.323e-01 7.087e-02 -1.867 0.061954 .
## stat13 -1.357e-01 7.014e-02 -1.934 0.053127 .
## stat87 -1.361e-01 7.068e-02 -1.926 0.054127 .
## x14 -1.558e-01 9.169e-02 -1.700 0.089271 .
## stat19 1.212e-01 7.031e-02 1.724 0.084739 .
## stat35 -1.160e-01 7.058e-02 -1.643 0.100364
## stat45 -1.319e-01 7.010e-02 -1.882 0.059947 .
## stat158 -1.094e-01 7.132e-02 -1.534 0.125052
## stat156 1.204e-01 7.064e-02 1.705 0.088273 .
## stat199 1.204e-01 6.977e-02 1.726 0.084460 .
## stat33 -1.172e-01 7.010e-02 -1.671 0.094699 .
## stat70 1.315e-01 6.994e-02 1.880 0.060136 .
## stat207 1.217e-01 7.043e-02 1.729 0.083910 .
## stat204 -1.196e-01 6.990e-02 -1.710 0.087263 .
## stat25 -1.149e-01 7.022e-02 -1.636 0.101836
## stat22 -1.152e-01 7.066e-02 -1.631 0.102932
## stat144 1.057e-01 7.007e-02 1.509 0.131337
## stat38 1.128e-01 7.039e-02 1.602 0.109216
## stat146 -1.119e-01 7.088e-02 -1.579 0.114324
## stat3 1.065e-01 7.031e-02 1.514 0.130045
## stat60 1.138e-01 7.034e-02 1.618 0.105814
## x12 -8.273e-02 5.316e-02 -1.556 0.119704
## stat89 -1.084e-01 6.997e-02 -1.549 0.121395
## stat10 -1.033e-01 7.071e-02 -1.461 0.144074
## stat175 -1.035e-01 7.046e-02 -1.468 0.142078
## stat141 1.011e-01 7.001e-02 1.445 0.148626
## stat161 1.003e-01 7.071e-02 1.419 0.155930
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.401 on 5946 degrees of freedom
## Multiple R-squared: 0.236, Adjusted R-squared: 0.229
## F-statistic: 33.4 on 55 and 5946 DF, p-value: < 2.2e-16
##
## [1] "Time taken for Forward Selection: 2.17501091559728"
## [1] "Number of data points that have Cook's D > 4/n: 280"
## [1] "Number of data points that have Cook's D > 1: 0"## 2689 2932 173 4452 7385
## 1.087513e-04 1.463362e-05 1.001286e-05 4.241730e-04 4.401662e-04
## 9881 3952 756 9468 8265
## 1.004612e-04 5.509666e-05 3.187433e-04 1.309107e-04 2.266537e-04
## 7775 3239 5947 2569 8467
## 2.691584e-06 1.310655e-05 4.315783e-05 9.489196e-04 2.659074e-05
## 7082 5633 3086 5522 4138
## 2.559434e-06 1.037786e-06 1.806729e-05 5.448409e-06 8.701204e-07
## 2063 8461 4679 7746 427
## 3.047791e-05 8.256194e-05 9.216213e-07 1.148647e-04 9.475194e-06
## 3969 3017 7362 2616 3755
## 1.414306e-06 1.291488e-06 1.909557e-04 2.626489e-04 2.414668e-04
## 4718 8312 3452 6027 3293
## 2.109043e-04 5.676526e-05 1.099863e-05 6.474206e-05 5.735727e-07
## 3639 5815 2208 7079 2625
## 1.485814e-05 1.373470e-05 6.206363e-04 6.621525e-05 5.099844e-05
## 3341 1938 9416 2433 1432
## 1.666065e-05 1.430575e-07 3.749981e-05 1.698697e-04 7.608247e-05
## 8296 167 9527 5785 7
## 7.391478e-05 1.562447e-05 7.151549e-06 3.539588e-05 9.882599e-04
## 9962 5854 143 2754 4668
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## 6.999105e-05 6.659605e-05 2.319424e-05 8.630459e-05 5.590157e-04
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## 2.516685e-06 1.029460e-04 1.103417e-04 3.561957e-05 3.779002e-05
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## 4.659494e-05 4.491211e-05 9.820129e-04 2.475319e-04 2.423014e-05
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## 7.626481e-05 1.492569e-05 1.167768e-04 2.558917e-06 9.568771e-03
## 1636 1725 3233 2692 165
## 1.076004e-05 1.101137e-04 1.998777e-04 5.986672e-05 6.282001e-07
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## 1235 6290 5832 8007 4906
## 1.383533e-05 2.784846e-04 9.843106e-07 8.140195e-06 7.072496e-05
## 8661 2746 8969 1935 7541
## 7.422395e-05 7.542744e-06 6.648682e-07 3.514075e-05 2.371408e-07
## 6121 3634 6692 612 7550
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## 2270 3531 2245 9885 5124
## 9.893095e-05 9.467718e-04 5.897831e-05 5.881935e-05 3.912674e-05
## 7008 505 8018 3849 7534
## 1.208809e-04 4.333856e-06 1.210278e-05 6.293508e-05 2.366207e-05
## 6331 4318 3429 6534 6663
## 5.739217e-06 2.849540e-09 1.606152e-05 1.524879e-04 4.298669e-06
## 2726 7151 8466 7167 5812
## 2.242672e-05 1.422621e-04 7.532569e-05 5.538748e-05 1.177259e-04
## 1480 3314 7485 9318 1405
## 8.314318e-05 1.117142e-04 3.142134e-04 1.076277e-05 5.084678e-04
## 4389 5882 1382 7165 4471
## 6.699164e-05 4.733900e-06 5.715518e-06 5.262122e-05 7.644667e-05
## 5711 8521 1140 9346 6032
## 6.090598e-09 4.552491e-05 1.055217e-04 3.135458e-05 9.986569e-05
## 6851 2606 8464 7978 8036
## 8.869577e-05 4.757918e-05 2.992232e-06 1.278930e-04 1.058797e-05
## 8217 8739 7561 9584 1922
## 5.088077e-05 4.773391e-05 8.269694e-04 6.618143e-06 1.267386e-06
## 5589 8035 4255 4676 8671
## 1.225688e-04 1.504041e-04 2.720854e-04 1.456912e-04 1.486069e-05
## 9399 4765 4200 6926 1695
## 3.512892e-05 4.932300e-05 1.190567e-04 1.839153e-06 3.885289e-04
## 9993 2118 7888 8979 4771
## 2.396958e-04 6.085026e-05 4.146948e-05 1.348213e-05 1.218045e-04
## 604 9690 7989 4396 6832
## 9.392849e-05 5.100635e-06 6.181649e-05 1.224610e-04 2.572178e-05
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## 3.639466e-05 1.286539e-04 6.862573e-10 7.438005e-04 4.845833e-05
## 4101 6007 1785 5500 7085
## 3.651748e-05 6.843533e-04 1.945032e-04 2.456776e-04 1.675447e-05
## 2452 8733 8611 6182 5429
## 4.984547e-07 8.367095e-05 2.487106e-06 3.637326e-04 9.962140e-05
## 5149 8407 4781 3702 7475
## 2.939497e-04 1.730606e-05 1.900309e-05 1.828845e-04 4.081417e-05
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## 2.468274e-04 1.407243e-04 7.890181e-04 7.248925e-05 7.667663e-05
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## 2.121220e-04 5.739293e-05 6.881046e-06 1.567247e-04 5.356990e-05
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## 6525 7988 3590 396 7548
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## 2145 7243 2836 5564 101
## 1.200957e-04 1.472784e-04 7.598433e-05 1.372691e-04 6.534377e-07
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## 6.937157e-05 2.572298e-06 6.814457e-04 9.499374e-05 2.112374e-05
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## 3.601180e-06 2.982455e-06 1.249187e-05 7.570825e-04 7.318326e-05
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## 1701 7804 854 2354 4619
## 3.090676e-04 1.761817e-07 3.088731e-05 4.217183e-05 2.021820e-05
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## 3.238338e-04 1.879585e-04 1.056956e-03 9.298648e-04 1.061770e-05
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## 2.214114e-04 1.043081e-04 3.530312e-06 2.339358e-05 1.364492e-04
## 9426 490 7557 9530 8727
## 2.676731e-05 1.517511e-05 1.994555e-04 1.415538e-05 1.212551e-04
## 8131 1842 4025 4627 5160
## 1.188418e-04 7.430719e-08 1.617962e-06 5.979320e-06 1.034188e-05
## 7673 4572 988 7547 9053
## 3.459614e-07 1.984898e-04 2.319065e-06 1.926782e-04 7.528271e-05
## 5243 3126 1829 8592 7684
## 8.445262e-05 1.446806e-05 8.446179e-06 1.050813e-04 1.458620e-06
## 2146 1184 6617 2283 3020
## 1.655633e-06 1.498453e-04 2.370932e-04 3.045386e-06 8.588949e-05
## 9804 3546 8424 2324 8542
## 4.118099e-05 1.040807e-06 3.990035e-04 7.998208e-05 6.686754e-07
## 2044 6932 2561 8981 4124
## 1.879371e-04 3.071817e-07 3.539118e-07 4.252871e-05 2.374700e-04
## 3353 8306 5546 1060 1610
## 2.674715e-05 7.956336e-04 1.764541e-04 3.353731e-05 1.008318e-05
## 346 1319 387 3991 7185
## 1.722671e-04 2.408532e-05 2.355219e-07 2.753394e-06 8.849346e-05
## 307 7671 1035 1108 1467
## 5.943610e-04 9.165955e-04 1.599628e-04 2.648571e-05 6.545223e-05
## 3189 9366 2186 6909 4973
## 4.282449e-04 1.260424e-04 2.857319e-04 6.668442e-08 2.385098e-05
## 8095 4734 9552 1713 2637
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## 7.793546e-07 1.372100e-05 1.108323e-04 2.649654e-06 1.898451e-05
## 6371 7252 1418 8053 5314
## 6.199713e-05 3.735329e-05 4.869621e-07 5.732661e-05 1.884460e-04
## 7559 8988 7030 1388 8916
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## 6384 6862 9479 6573 6854
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## 8759 5745 8595 968 420
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## 28 5302 8344 5734 3800
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## 2487 5877 3116 6770 8013
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## 3.000274e-06 3.881046e-04 4.924061e-05 2.384992e-04 2.453999e-05
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## 2.836154e-05 2.577187e-04 4.135143e-05 4.298116e-07 1.700584e-04
## 727 5506 9477 2587 7175
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## 6303 4096 1269 3157 1586
## 1.733022e-04 6.425180e-07 4.101077e-05 2.609796e-06 1.910440e-04
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## 122 4495 3039 9040 3920
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## 1.695672e-04 2.790455e-05 2.550262e-04 5.066315e-05 2.840198e-05
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## 4.631437e-05 2.042721e-05 1.264957e-05 1.424773e-04 3.040419e-05
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## 2.056199e-04 2.407097e-05 7.954917e-05 1.517442e-05 1.474504e-04
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## 9676 418 9847 7189 5318
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## 4658 4552 666 6626 3685
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## 9371 6454 1284 1781 7726
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## 8941 4270 3798 9224 4595
## 2.192855e-05 5.315657e-05 3.374159e-06 8.552880e-05 6.989845e-06
## 4027 655 1598 4975 5693
## 9.855108e-04 6.023090e-05 3.887991e-05 1.968766e-05 1.397134e-05
## 6693 2514 1249 7286 6009
## 1.527489e-04 1.670551e-04 1.370297e-04 9.796081e-05 1.988761e-05
## 6267 6545 297 8608 5191
## 1.252514e-03 1.553723e-04 1.388671e-04 4.600780e-04 2.172980e-04
## 7229 7757 5694 7391 362
## 5.557685e-05 3.571924e-05 1.622594e-06 1.907749e-05 1.034291e-05
## 7358 7158 3929 8340 3450
## 8.548595e-06 2.340208e-04 7.555120e-06 1.338431e-06 4.018364e-05
## 8508 5279 9100 1243 5511
## 2.255664e-04 4.468265e-06 2.211131e-05 2.316001e-04 5.745754e-07
## 4346 5796 5130 5060 8703
## 3.075738e-04 1.167143e-04 2.284942e-04 1.527700e-04 8.003356e-05
## 2038 5122 5208 7446 1700
## 6.203505e-05 1.064864e-05 2.424010e-05 1.623170e-04 8.965601e-05
## 9558 8420 6293 2971 5601
## 7.503005e-05 2.558890e-04 1.088993e-04 4.897624e-05 4.513481e-06
## 5458 8841 4371 7261 3272
## 1.679466e-04 5.128558e-07 3.391425e-06 2.444167e-04 5.457669e-06
## 1337 4967 2120 7021 6176
## 3.654472e-04 2.823296e-05 9.652105e-06 2.414767e-05 9.257157e-05
## 5550 9664 2548 5480 4056
## 8.764407e-05 1.331821e-04 3.325602e-04 1.179611e-06 4.976246e-06
## 9707 8019 2097 1887 5195
## 1.033238e-08 5.041289e-05 1.125587e-04 1.396475e-04 1.125603e-04
## 7955 1774 4501 1908 2431
## 6.041813e-06 7.938673e-04 4.482695e-04 3.651609e-04 5.806602e-04
## 4412 8329 5226 9178 5099
## 2.437146e-07 2.612048e-04 3.306014e-05 2.607849e-05 2.628177e-06
## 9165 6265 1665 8331 4680
## 4.006141e-06 8.834580e-05 7.076537e-04 1.133730e-04 7.291756e-07
## 1439 4006 4252 4344 5097
## 7.613891e-06 7.736924e-07 1.180180e-04 3.494147e-04 3.331061e-05
## 6398 5980 2334 8696 2639
## 3.865969e-05 3.877764e-07 1.053098e-04 2.871971e-04 1.100358e-04
## 2043 3839 8980 5454 9168
## 2.550381e-05 3.616358e-05 1.257717e-07 6.880365e-06 5.610474e-05
## 8002 7527 3575 5056 8691
## 6.051189e-05 4.011800e-05 9.590376e-06 5.408312e-05 2.246809e-04
## 2760 5951 2225 1055 2855
## 5.381546e-06 1.060779e-04 2.135464e-05 1.368450e-04 6.840512e-05
## 1481 6102 1453 1139 6411
## 3.466526e-05 4.275687e-04 2.273170e-04 4.815169e-08 1.299227e-04
## 7249 7902 742 1419 2005
## 1.040119e-08 5.713523e-05 3.792120e-06 1.938151e-06 2.270850e-05
## 8472 2455 5800 8083 3673
## 5.090144e-04 1.372504e-04 1.230302e-04 4.580344e-05 2.331383e-04
## 8892 1228 2912 4100 7882
## 1.907926e-05 1.661512e-04 1.388309e-04 1.097202e-04 1.474355e-05
## 7081 4869 6709 1619 2203
## 1.186996e-05 2.693260e-05 1.604507e-04 6.238048e-06 1.220168e-07
## 1794 2137 1420 1267 8001
## 2.078237e-06 5.395465e-12 1.192000e-04 1.582151e-04 6.908901e-05
## 7667 9998 8286 5190 2400
## 6.900450e-06 2.116772e-03 1.949000e-04 7.580644e-04 8.090327e-04
## 3453 9306 947 8997 7397
## 6.154270e-05 3.421628e-04 5.266592e-04 5.685279e-05 1.377769e-04
## 80 7104 4403 2248 8064
## 1.418049e-04 6.229422e-05 1.769039e-03 4.475676e-05 3.295826e-04
## 8024 1207 9709 1942 667
## 4.149224e-05 1.205100e-05 7.104598e-06 4.688163e-05 1.288479e-05
## 650 5628 2603 466 7339
## 9.617283e-05 2.225599e-05 1.206472e-04 6.743937e-05 5.558621e-05
## 5111 3584 7951 9283 662
## 1.599657e-04 1.060368e-03 1.756013e-03 1.381123e-04 2.401632e-03
## 8716 7846 4150 8975 888
## 5.504900e-05 1.687230e-05 9.509910e-07 6.367732e-05 1.900973e-05
## 5865 7889 411 1272 102
## 5.006562e-05 3.502746e-04 5.736031e-05 8.388277e-05 1.843129e-06
## 2205 3178 5531 6238 2645
## 6.061548e-05 1.961282e-07 7.334898e-05 1.275158e-04 3.448651e-05
## 5366 7865 4149 4167 1849
## 7.776140e-05 7.646609e-05 3.774067e-04 3.566961e-04 2.136436e-04
## 3894 2031 1248 380 7204
## 6.788758e-06 2.238869e-05 3.408815e-06 1.015805e-05 4.369703e-03
## 7370 3856 887 3833 3818
## 2.179008e-05 2.824576e-04 4.543040e-04 1.147142e-04 2.751840e-04
## 3257 8428 1766 1571 9749
## 2.135273e-04 9.358113e-05 3.268871e-05 8.531076e-05 2.523345e-05
## 3652 1136 9490 3283 6125
## 4.027364e-05 7.288362e-05 2.555477e-05 1.545508e-04 2.416558e-08
## 6910 4060 8500 1386 8747
## 8.831395e-05 3.572501e-04 5.121848e-07 5.461973e-07 1.297699e-04
## 9646 4423 3219 5266 7502
## 1.321115e-03 1.196545e-03 6.826300e-06 7.662443e-06 2.035481e-05
## 9759 7583 1514 3937 4669
## 1.803851e-04 2.032533e-04 2.879821e-04 6.706928e-07 2.586022e-04
## 6480 6338 1341 1580 6695
## 9.849895e-04 3.513976e-03 3.402567e-04 3.566867e-04 1.454166e-07
## 6078 9781 4634 5502 1081
## 1.368879e-05 5.183018e-06 4.671627e-10 9.473804e-05 4.003927e-05
## 2004 7098 922 7632 845
## 2.674260e-04 1.151187e-04 2.509705e-03 6.994178e-06 7.695408e-05
## 7950 1037 5053 2444 5251
## 5.189236e-05 1.448728e-05 2.213978e-04 1.757133e-04 3.242023e-03
## 7880 2350 8040 9357 6423
## 1.144209e-06 1.565736e-05 2.019047e-05 5.008355e-09 1.031551e-05
## 1221 3705 7783 4610 5249
## 1.802098e-05 8.422158e-05 7.076688e-07 7.778502e-05 1.137828e-05
## 759 9986 8264 771 1312
## 8.926559e-08 2.067669e-04 2.935906e-05 7.578524e-05 1.437834e-04
## 8402 91 4907 1991 7461
## 1.488198e-04 4.092873e-05 2.210828e-04 2.731525e-05 2.036054e-04
## 3725 6347 1075 9642 2436
## 2.276999e-04 2.745747e-03 8.479179e-06 2.998970e-05 9.192722e-10
## 9066 7748 7996 4266 9582
## 2.614601e-05 5.604656e-06 3.379820e-04 2.221602e-05 2.482677e-06
## 2642 2621 6958 5175 8641
## 1.091873e-03 1.725542e-04 6.615206e-07 5.531720e-06 1.776460e-07
## 1937 9500 4566 9814 7300
## 1.249161e-04 1.680539e-04 6.901211e-08 1.289994e-06 2.076625e-05
## 2468 7777 5837 5273 5312
## 4.447056e-07 3.853907e-04 9.163229e-05 1.108769e-04 1.898042e-05
## 9779 3904 9145 7751 5311
## 1.099414e-04 5.166298e-06 7.502049e-04 2.605903e-04 7.850640e-04
## 4937 7878 5354 175 5415
## 1.755174e-05 7.499108e-07 2.013105e-04 1.465223e-06 5.118998e-05
## 2363 6308 1034 9470 2653
## 3.434692e-05 1.850317e-07 3.227223e-05 8.919064e-06 8.072801e-05
## 2540 9158 6188 72 7374
## 1.878571e-07 7.866008e-06 7.539160e-05 2.727789e-05 1.862678e-03
## 8362 6967 8863 1394 1808
## 1.100386e-03 1.093988e-04 4.838360e-05 2.593635e-04 3.811410e-05
## 649 4815 388 2850 1681
## 1.238051e-04 6.344548e-04 3.513389e-05 3.990239e-06 5.219381e-05
## 4113 795 7758 6174 9458
## 4.542931e-04 7.656234e-05 4.153443e-04 1.127980e-04 8.441476e-05
## 8413 6828 7235 3788 8884
## 7.656792e-04 1.667297e-06 7.063902e-06 1.923048e-04 2.074962e-05
## 7962 238 1385 5467 7078
## 2.696423e-07 5.848907e-05 2.140504e-05 7.914123e-05 2.425413e-07
## 441 7453 1080 5922 3268
## 1.031538e-03 3.757104e-05 1.543811e-04 8.682999e-06 1.226949e-06
## 6391 9213 7200 3903 8734
## 8.023797e-06 1.510012e-06 2.019748e-04 7.203985e-08 9.394723e-05
## 9653 6495 6652 5329 3540
## 5.245717e-05 1.617346e-03 4.523755e-06 7.325648e-05 1.192764e-05
## 2430 6776 6037 6117 9967
## 1.739475e-06 5.597665e-05 1.505194e-04 4.819756e-05 1.013014e-05
## 778 6759 9864 8257 7788
## 1.670736e-04 4.352197e-05 3.932689e-06 3.625850e-05 2.164503e-06
## 4635 3500 6704 8112 9248
## 2.757672e-05 2.554923e-06 2.337509e-04 1.249668e-04 2.239122e-07
## 5973 9043 5651 8878 8914
## 2.090065e-06 1.880362e-04 1.632367e-04 3.959347e-05 2.962489e-05
## 6413 4810 1383 5051 6217
## 9.595950e-06 8.156070e-05 2.343936e-03 2.137054e-05 8.894810e-05
## 3838 5306 226 8745 8172
## 6.254931e-05 1.222391e-04 2.863696e-05 8.170848e-06 2.103503e-05
## 3567 4394 9921 9219 2493
## 4.058738e-05 2.184958e-07 4.911840e-05 1.513991e-04 6.199113e-04
## 4787 9202 2409 8122 1308
## 1.810823e-05 7.114127e-05 7.157955e-05 1.939165e-04 1.884749e-04
## 2989 21 4057 2875 9354
## 1.018609e-04 4.897417e-05 5.214197e-05 6.822980e-05 4.805854e-04
## 2233 3179 651 9088 2365
## 2.020992e-04 1.342917e-04 3.043277e-04 5.180844e-04 1.451066e-07
## 6935 3320 8528 4893 4838
## 1.852695e-05 1.689905e-05 3.763461e-05 9.321998e-09 1.632759e-05
## 7001 6731 3209 3160 974
## 9.329432e-05 6.195079e-05 6.136646e-04 1.605570e-04 2.031344e-06
## 2651 2638 8740 948 9562
## 9.960754e-05 3.427582e-05 3.807421e-04 3.472597e-05 6.866732e-05
## 8767 8584 8774 6996 8193
## 2.042424e-04 3.699373e-05 1.578742e-04 5.482068e-06 5.205531e-05
## 4325 9716 4286 5225 7614
## 1.504732e-04 5.709855e-05 7.803006e-05 4.122879e-04 1.492606e-05
## 7256 5228 3031 2498 60
## 7.564848e-05 6.971947e-05 4.216006e-06 1.694740e-06 7.159788e-05
## 5283 5079 3780 2965 9241
## 1.959352e-05 2.562939e-04 2.248018e-05 3.603867e-07 4.159055e-04
## 4136 2192 2195 5770 8847
## 1.698163e-04 1.567511e-05 8.757468e-05 2.153631e-04 2.124623e-05
## 2533 5940 5052 9654 9176
## 1.680023e-05 2.357128e-05 2.170136e-05 1.800666e-06 1.321085e-06
## 2335 8032 9023 4260 1692
## 9.106947e-05 2.611544e-04 3.733621e-05 7.348351e-07 1.298175e-05
## 5674 1470 1755 5381 5835
## 6.621162e-04 2.755950e-05 1.224943e-04 1.665968e-06 1.214270e-04
## 8893 304 5141 2168 7303
## 2.836472e-05 3.139509e-05 1.163690e-05 8.621672e-05 5.265708e-04
## 2364 5147 8494 8044 5620
## 4.376445e-05 1.032772e-03 2.097444e-06 4.078986e-06 1.335469e-03
## 4077 9083 4424 5804 3472
## 1.000886e-04 9.876702e-06 3.357805e-05 2.232024e-04 1.449073e-04
## 5596 8811 6252 1745 2770
## 2.238001e-06 4.042281e-05 2.362917e-04 1.361672e-04 5.841400e-05
## 4963 4171 9822 8203 6771
## 2.313754e-04 3.842917e-05 3.527714e-04 1.437378e-06 1.753333e-04
## 8593 447 892 8782 9410
## 2.940702e-05 9.289760e-06 2.502325e-04 1.315188e-04 7.850448e-05
## 4913 158 6343 9162 7744
## 1.187467e-04 2.786619e-04 9.736616e-07 3.361345e-06 1.396638e-03
## 3379 691 5423 4851 18
## 9.178043e-05 1.336523e-04 3.985573e-05 2.002384e-05 6.153169e-07
## 5417 2419 1861 5428 392
## 4.335326e-06 3.833517e-06 4.171817e-06 1.307325e-05 6.395296e-05
## 8323 1927 960 4298 1019
## 3.734899e-05 7.261628e-05 3.655594e-06 5.050795e-04 1.862574e-07
## 5303 4731 6183 4317 2276
## 1.270143e-04 6.212847e-05 5.534235e-04 2.081649e-06 1.182279e-05
## 3069 7639 4877 4889 9737
## 1.478964e-05 9.050989e-04 2.142260e-04 9.889028e-07 3.733916e-05
## 3397 404 7526 9009 903
## 1.411671e-05 3.851893e-06 5.143015e-05 1.708178e-03 7.472253e-06
## 4219 3408 8574 8713 96
## 1.012806e-04 5.512897e-06 4.112630e-04 1.138835e-04 9.209195e-06
## 1550 3147 5103 6322 2737
## 2.201192e-05 5.669865e-05 1.003557e-05 1.856459e-05 1.601390e-06
## 2148 4835 137 4949 7360
## 1.649584e-04 1.343548e-04 1.090687e-04 1.950438e-05 4.239880e-06
## 4287 4247 9135 6566 5387
## 9.537473e-06 8.769655e-05 7.807977e-05 1.860768e-04 1.768244e-04
## 2413 8568 9917 4302 8712
## 2.687195e-04 9.758869e-06 2.481650e-04 1.445908e-07 4.075761e-05
## 5773 6264 5636 6298 2915
## 5.118979e-04 1.214170e-04 5.442296e-05 1.673649e-04 1.466398e-03
## 4308 8615 4373 9568 7493
## 3.334525e-05 2.787920e-04 1.421553e-05 5.686080e-06 3.079436e-04
## 2162 3923 9845 8037 6130
## 1.158146e-05 1.004805e-04 9.396593e-08 3.994660e-04 1.770117e-05
## 2411 3758 1186 3114 7241
## 4.399840e-06 1.270157e-06 6.095471e-05 2.712518e-04 1.382759e-06
## 3465 3369 5335 5477 1724
## 1.150467e-05 1.933215e-04 2.630981e-07 1.496484e-04 9.484971e-06
## 1886 1251 472 2860 9356
## 1.353277e-05 3.906969e-05 6.183769e-05 1.705640e-04 9.082086e-06
## 4273 228 3941 849 3884
## 2.145415e-04 8.304781e-05 1.634946e-04 8.226472e-05 1.098004e-04
## 2157 3187 1047 8436 7605
## 4.162555e-05 8.586740e-05 5.179697e-05 2.087838e-04 3.863797e-05
## 5222 1491 942 3732 3840
## 6.027706e-08 5.757649e-04 5.661612e-05 8.969971e-04 1.434938e-05
## 580 4177 334 7812 1796
## 3.282293e-04 3.130300e-05 2.298187e-04 2.015570e-04 4.325022e-05
## 7424 7293 8812 7197 4063
## 5.765518e-06 2.882148e-04 1.763060e-04 1.567073e-04 1.897416e-08
## 1959 1772 8604 7353 8678
## 2.049385e-05 1.410146e-04 1.575799e-03 9.345829e-05 2.293815e-03
## 5377 4932 7732 1652 9120
## 2.705250e-05 3.050074e-07 7.411941e-05 4.059162e-06 6.365558e-08
## 6425 5260 7867 6836 4319
## 9.489343e-05 3.589775e-04 3.424785e-04 7.406678e-05 1.121568e-04
## 5640 4516 1212 234 4653
## 2.942854e-05 8.143681e-05 5.539998e-06 2.275112e-03 3.662987e-05
## 4958 7010 6486 9698 5164
## 1.681599e-05 5.145189e-05 8.811104e-04 9.895040e-05 1.544583e-06
## 5401 7160 1172 5605 4209
## 4.652101e-05 1.614021e-04 5.920417e-04 1.061814e-05 2.083953e-05
## 1875 7436 271 6028 9571
## 9.549018e-06 2.292029e-06 9.212449e-06 2.302294e-04 1.614632e-04
## 5359 5834 3659 5398 5069
## 6.043355e-04 4.767967e-05 5.500156e-05 4.694511e-05 1.019493e-04
## 1642 714 8785 1233 4361
## 9.043846e-04 3.724961e-06 9.135027e-05 2.421069e-04 6.284599e-05
## 1837 6620 4388 8931 6599
## 2.995406e-04 2.674700e-04 1.887765e-04 1.543656e-04 1.514986e-08
## 1693 3074 3927 7034 1817
## 6.465640e-06 4.721989e-06 2.374528e-05 2.096664e-05 2.243970e-05
## 4462 8698 6782 7460 3782
## 3.795559e-05 7.151388e-05 3.162887e-04 1.997300e-06 9.248060e-05
## 315 8169
## 1.068044e-04 5.292948e-06Test
if (algo.forward == TRUE){
test.model(model.forward, data.test, "Forward Selection")
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 111.4 121.7 125.2 125.2 128.7 143.4
## [1] "Forward Selection Test MSE: 95.6720383423728"
Forward Selection (w/ filtered train)
Train
if (algo.forward == TRUE){
t1 = Sys.time()
model.forward2 = step(model.null2, scope=list(lower=model.null2, upper=model.full2), direction="forward", trace = 0)
print(summary(model.forward2))
#saveRDS(model.forward,file = "model_forward.rds")
t2 = Sys.time()
print (paste("Time taken for Forward Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.forward2, data.train2)
}##
## Call:
## lm(formula = y3 ~ sqrt.x18 + x7 + stat98 + stat110 + x9 + x4 +
## x10 + x16 + x17 + x8 + stat14 + x11 + stat172 + x21 + stat128 +
## stat26 + stat41 + stat4 + stat146 + stat23 + stat54 + stat127 +
## stat87 + stat100 + stat99 + stat141 + stat15 + stat38 + stat50 +
## stat70 + stat13 + stat62 + stat144 + x23 + stat156 + stat3 +
## stat39 + x13 + stat35 + x5 + stat91 + stat167 + stat207 +
## stat194 + stat92 + stat34 + stat216 + stat73 + stat10 + stat33 +
## x6 + stat149 + stat214 + stat80 + stat60 + stat61 + stat48 +
## stat5 + stat183 + stat43 + stat46 + stat175 + stat199 + stat95,
## data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.9225 -5.1249 -0.9933 4.6601 21.1984
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.562e+01 1.955e+00 43.805 < 2e-16 ***
## sqrt.x18 7.127e+00 2.102e-01 33.907 < 2e-16 ***
## x7 3.290e+00 1.428e-01 23.035 < 2e-16 ***
## stat98 9.302e-01 5.457e-02 17.048 < 2e-16 ***
## stat110 -8.844e-01 5.536e-02 -15.974 < 2e-16 ***
## x9 9.363e-01 7.425e-02 12.610 < 2e-16 ***
## x4 -1.601e-02 2.026e-03 -7.901 3.31e-15 ***
## x10 4.360e-01 6.895e-02 6.323 2.76e-10 ***
## x16 2.616e-01 4.811e-02 5.438 5.62e-08 ***
## x17 4.053e-01 7.285e-02 5.563 2.77e-08 ***
## x8 1.604e-01 3.325e-02 4.825 1.44e-06 ***
## stat14 -2.740e-01 5.487e-02 -4.993 6.11e-07 ***
## x11 6.695e+07 1.653e+07 4.049 5.20e-05 ***
## stat172 2.020e-01 5.543e-02 3.645 0.00027 ***
## x21 3.396e-02 9.472e-03 3.585 0.00034 ***
## stat128 -1.668e-01 5.552e-02 -3.005 0.00267 **
## stat26 -1.653e-01 5.559e-02 -2.974 0.00295 **
## stat41 -1.541e-01 5.520e-02 -2.792 0.00526 **
## stat4 -1.461e-01 5.600e-02 -2.609 0.00910 **
## stat146 -1.538e-01 5.598e-02 -2.747 0.00603 **
## stat23 1.302e-01 5.518e-02 2.359 0.01837 *
## stat54 -1.571e-01 5.619e-02 -2.795 0.00521 **
## stat127 -1.381e-01 5.536e-02 -2.494 0.01267 *
## stat87 -1.357e-01 5.587e-02 -2.428 0.01521 *
## stat100 1.365e-01 5.567e-02 2.452 0.01424 *
## stat99 1.242e-01 5.590e-02 2.221 0.02638 *
## stat141 1.159e-01 5.525e-02 2.098 0.03593 *
## stat15 -1.468e-01 5.484e-02 -2.677 0.00744 **
## stat38 1.339e-01 5.555e-02 2.411 0.01594 *
## stat50 1.238e-01 5.510e-02 2.246 0.02472 *
## stat70 1.269e-01 5.520e-02 2.299 0.02152 *
## stat13 -1.207e-01 5.540e-02 -2.178 0.02944 *
## stat62 -1.285e-01 5.568e-02 -2.308 0.02106 *
## stat144 1.107e-01 5.524e-02 2.005 0.04502 *
## x23 1.543e-01 7.377e-02 2.092 0.03649 *
## stat156 1.119e-01 5.575e-02 2.008 0.04470 *
## stat3 1.087e-01 5.549e-02 1.959 0.05017 .
## stat39 -1.011e-01 5.533e-02 -1.828 0.06761 .
## x13 3.415e-02 1.691e-02 2.019 0.04352 *
## stat35 -1.181e-01 5.588e-02 -2.113 0.03467 *
## x5 1.209e-01 6.614e-02 1.828 0.06767 .
## stat91 -1.044e-01 5.520e-02 -1.892 0.05856 .
## stat167 -1.059e-01 5.552e-02 -1.908 0.05649 .
## stat207 1.013e-01 5.552e-02 1.825 0.06806 .
## stat194 -1.071e-01 5.565e-02 -1.925 0.05427 .
## stat92 -1.006e-01 5.566e-02 -1.807 0.07080 .
## stat34 9.884e-02 5.554e-02 1.780 0.07519 .
## stat216 -1.027e-01 5.535e-02 -1.856 0.06354 .
## stat73 1.013e-01 5.591e-02 1.812 0.07010 .
## stat10 -9.745e-02 5.590e-02 -1.743 0.08131 .
## stat33 -1.003e-01 5.536e-02 -1.812 0.07011 .
## x6 -2.284e-01 1.330e-01 -1.718 0.08584 .
## stat149 -9.527e-02 5.613e-02 -1.697 0.08970 .
## stat214 -9.777e-02 5.558e-02 -1.759 0.07860 .
## stat80 9.089e-02 5.604e-02 1.622 0.10491
## stat60 9.114e-02 5.561e-02 1.639 0.10126
## stat61 -8.200e-02 5.567e-02 -1.473 0.14080
## stat48 8.846e-02 5.607e-02 1.578 0.11469
## stat5 -8.212e-02 5.557e-02 -1.478 0.13952
## stat183 8.168e-02 5.544e-02 1.473 0.14071
## stat43 -8.342e-02 5.572e-02 -1.497 0.13443
## stat46 8.266e-02 5.576e-02 1.482 0.13830
## stat175 -8.201e-02 5.557e-02 -1.476 0.14003
## stat199 7.870e-02 5.509e-02 1.429 0.15317
## stat95 7.934e-02 5.557e-02 1.428 0.15344
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.243 on 5656 degrees of freedom
## Multiple R-squared: 0.3403, Adjusted R-squared: 0.3329
## F-statistic: 45.6 on 64 and 5656 DF, p-value: < 2.2e-16
##
## [1] "Time taken for Forward Selection: 2.86280791759491"
## [1] "Number of data points that have Cook's D > 4/n: 297"
## [1] "Number of data points that have Cook's D > 1: 0"## 2689 2932 173 4452 7385
## 1.406985e-04 7.746847e-06 4.177321e-07 5.994964e-04 7.529870e-04
## 9881 3952 756 9468 8265
## 2.917612e-04 1.769659e-04 4.276105e-04 1.755994e-04 5.622964e-04
## 7775 3239 5947 8467 7082
## 4.379534e-06 1.720987e-05 9.652645e-05 5.799684e-05 7.354877e-05
## 5633 3086 5522 4138 2063
## 4.808659e-05 4.093509e-05 1.272508e-06 1.286740e-05 1.509886e-04
## 8461 4679 7746 427 3969
## 2.222129e-04 5.020931e-09 6.404333e-05 1.449014e-05 5.652728e-07
## 3017 7362 2616 3755 4718
## 8.079964e-05 2.388151e-04 4.386723e-04 1.957599e-04 3.837273e-04
## 8312 3452 6027 3293 3639
## 4.581768e-05 1.560051e-05 2.476527e-04 5.911841e-06 1.824008e-05
## 5815 7079 2625 3341 1938
## 6.866781e-06 1.011945e-04 2.135760e-05 2.629151e-05 1.066805e-05
## 9416 2433 1432 8296 167
## 1.012657e-04 2.453721e-04 3.462084e-04 6.508701e-05 1.928547e-05
## 9527 5785 9962 5854 143
## 7.310169e-06 1.646083e-04 3.890554e-04 3.991789e-05 5.174911e-04
## 2754 4668 2752 6784 4555
## 3.285854e-04 3.318643e-06 3.072808e-04 5.753381e-05 7.428073e-05
## 611 5716 1086 8052 9675
## 6.430007e-04 3.698501e-06 1.819177e-06 1.791903e-05 1.627931e-04
## 950 2339 352 2155 5945
## 2.343321e-04 3.147447e-05 1.011397e-04 6.268621e-04 1.712210e-04
## 9245 2909 5238 7521 8596
## 1.062654e-04 1.112441e-04 1.114748e-04 1.678899e-04 2.811965e-05
## 4129 2669 5919 2016 8599
## 9.660562e-04 3.245110e-05 2.675400e-04 4.892882e-04 6.956873e-05
## 3309 1958 1438 2206 6462
## 1.227557e-04 2.881642e-05 3.724685e-04 3.424093e-04 9.171825e-04
## 623 6643 1673 5777 8908
## 8.135407e-05 9.557157e-05 9.508983e-04 3.622757e-04 1.469664e-04
## 7184 2943 6118 2104 2082
## 3.685601e-05 1.843982e-05 8.091568e-05 1.784845e-04 8.101077e-04
## 2663 67 1458 9256 5808
## 1.935129e-04 2.546976e-04 4.418753e-07 6.515587e-06 1.245217e-05
## 1017 6976 5582 1371 8657
## 1.914181e-06 1.848014e-05 3.449675e-06 4.620611e-04 2.343408e-04
## 2085 8652 438 5379 7528
## 1.224469e-03 2.191696e-05 1.552221e-05 3.016529e-05 6.091051e-04
## 1679 8994 2196 2956 3982
## 1.707443e-04 5.079739e-04 6.412070e-07 3.609312e-05 1.272725e-04
## 4827 9197 2918 4522 17
## 1.008515e-04 7.258219e-05 4.436874e-06 3.593063e-04 8.712974e-05
## 4012 4051 1395 1542 7802
## 4.729345e-05 8.042264e-05 2.801922e-04 2.200398e-05 1.235711e-04
## 7192 3690 7044 7072 4985
## 4.289409e-05 3.558110e-04 2.092043e-06 4.017154e-05 2.331079e-04
## 6191 816 6005 311 8448
## 4.882155e-05 1.583453e-04 7.479025e-04 1.552145e-04 3.758022e-06
## 7601 4753 1663 5955 7307
## 7.187024e-04 1.697114e-04 8.892795e-09 1.856406e-03 1.083570e-04
## 2575 5151 7969 4819 7942
## 2.057814e-04 6.127752e-04 1.237387e-06 4.517119e-05 2.782542e-06
## 1786 8423 5697 7027 3073
## 5.110320e-04 3.009537e-04 1.779292e-04 8.135760e-05 3.638036e-06
## 9669 1720 1210 4441 3060
## 3.142798e-06 1.273934e-05 2.336437e-04 2.535036e-04 1.134396e-04
## 2734 6687 5231 2311 7499
## 3.455243e-04 2.520515e-06 1.534050e-04 6.313766e-07 4.534213e-08
## 629 5658 3622 4591 3699
## 1.678929e-05 1.187647e-04 1.918000e-04 4.096307e-04 1.233319e-07
## 964 6177 8861 689 4206
## 2.264289e-04 7.726082e-05 2.457331e-04 1.276750e-06 1.827836e-04
## 5004 5906 7834 6096 51
## 3.420110e-04 4.257205e-06 2.774820e-06 4.157449e-05 3.516834e-05
## 5683 5307 6700 2061 1839
## 1.112843e-04 7.646117e-05 3.337059e-07 1.658128e-05 3.590933e-05
## 8960 5074 5482 6212 9973
## 2.987047e-04 3.888424e-04 7.440272e-05 1.163408e-04 3.392748e-05
## 2755 7108 8983 3097 605
## 6.540050e-05 4.173268e-05 1.276394e-06 2.534392e-04 7.771674e-05
## 1732 7466 3675 2725 401
## 3.116793e-05 2.217373e-04 2.939236e-05 1.707327e-04 6.831484e-04
## 5200 9727 6001 53 7696
## 1.941928e-05 1.907862e-05 2.565083e-04 8.359319e-05 4.926637e-05
## 349 6129 8113 891 9427
## 1.778644e-04 7.308461e-05 5.624771e-04 4.232750e-04 6.950162e-04
## 1611 562 8692 5552 8519
## 1.617624e-05 1.051962e-03 3.013141e-04 7.357367e-05 3.583408e-05
## 9812 823 8915 9784 4764
## 2.582867e-04 6.406431e-05 1.181425e-05 4.216492e-05 1.018389e-05
## 643 1722 7095 4748 222
## 1.632572e-09 3.534427e-04 7.189841e-06 6.522106e-04 2.122533e-06
## 799 1584 2362 6152 2499
## 1.597114e-04 3.456258e-05 1.981356e-04 8.752688e-06 3.002387e-04
## 6519 7404 4205 4867 7645
## 2.491167e-05 1.467116e-04 5.331211e-08 6.119630e-05 1.548997e-05
## 8212 5404 530 283 2483
## 3.099297e-05 1.025799e-04 6.221952e-05 4.673707e-05 4.192548e-04
## 7709 4882 7554 7268 174
## 3.012743e-04 9.895095e-07 5.100334e-04 1.235494e-04 7.849968e-04
## 4649 984 4822 6506 4182
## 1.596033e-04 7.750488e-06 1.462458e-04 3.992831e-05 4.079638e-04
## 8190 7127 3038 2017 811
## 1.184307e-03 3.755620e-04 6.789055e-05 3.522988e-04 1.736136e-04
## 3784 9042 2423 3194 220
## 2.977181e-04 1.444113e-03 6.471565e-05 1.573324e-03 2.805375e-05
## 6852 7435 5548 4204 5165
## 2.112538e-06 7.508185e-05 3.377145e-04 9.638672e-06 5.955994e-05
## 2790 2386 6721 7459 509
## 7.239359e-05 2.262482e-06 3.085906e-04 2.611997e-04 1.163208e-04
## 992 2922 77 7284 8004
## 1.961970e-06 5.033252e-04 5.191450e-04 7.309150e-05 3.270088e-04
## 8443 1776 2954 8580 2821
## 3.425560e-04 8.295508e-07 3.629973e-05 1.107079e-05 5.876091e-05
## 2144 8843 1230 4435 7628
## 6.815323e-04 5.737546e-05 7.435570e-05 4.408472e-04 2.053596e-04
## 7312 9632 7807 884 9583
## 2.555450e-04 5.768824e-05 3.715304e-04 1.867598e-04 4.896429e-04
## 5396 3633 7178 2175 9067
## 9.080128e-07 1.917426e-06 3.520000e-05 5.315195e-05 1.594052e-04
## 6579 8752 8751 2115 1727
## 1.330924e-06 7.821418e-05 2.615642e-04 1.294819e-05 8.050807e-08
## 7900 6814 468 1934 2198
## 7.472983e-06 5.300421e-05 7.299742e-07 2.093374e-04 7.433346e-05
## 6858 1764 4314 272 55
## 2.967038e-04 3.933267e-04 1.734024e-04 7.685931e-05 8.296967e-05
## 9350 8588 6595 3371 3211
## 2.596585e-04 1.187184e-04 2.550551e-04 1.373376e-05 1.068616e-04
## 8473 7444 4074 5348 3821
## 7.782356e-04 9.111184e-04 6.195380e-04 6.261907e-06 5.798257e-05
## 8566 1941 4611 7730 9048
## 4.770926e-06 6.002217e-05 7.274131e-04 1.404716e-04 3.858594e-06
## 3498 5645 1771 5113 7344
## 3.153283e-04 4.956805e-04 2.328620e-06 1.863971e-07 1.186489e-03
## 3656 3708 6503 9504 5232
## 1.819703e-06 2.207314e-05 3.415575e-06 2.829673e-07 5.136399e-04
## 6440 9094 8998 5631 6446
## 1.060195e-04 5.275658e-05 2.776322e-04 1.132493e-04 6.938994e-07
## 3439 699 6934 4348 5700
## 2.070012e-04 2.091188e-04 4.101092e-04 9.273650e-05 1.267389e-04
## 2394 3312 7166 1278 5530
## 1.582039e-04 5.147273e-05 6.028294e-04 1.871226e-06 8.196714e-05
## 8343 3046 2808 6332 4337
## 2.350167e-04 4.814428e-04 8.573496e-05 7.769766e-05 1.868809e-05
## 8717 7699 3175 2516 4437
## 6.326983e-05 1.249278e-06 1.563817e-04 1.576173e-04 3.484426e-05
## 2972 5639 8202 6017 8950
## 8.621849e-05 9.861134e-05 6.696904e-04 1.657404e-04 2.060966e-04
## 1452 1194 8606 6139 8182
## 4.257541e-08 1.263477e-06 2.253364e-04 1.649827e-05 1.256227e-04
## 5662 2165 4673 8791 2865
## 1.540521e-05 2.496459e-05 1.360081e-05 6.216375e-04 8.553720e-05
## 9095 5357 2854 2126 5764
## 6.934886e-07 4.721596e-04 6.648918e-05 3.866065e-04 8.443955e-06
## 5015 5365 7454 2418 8124
## 5.268468e-06 4.748588e-05 2.029375e-04 1.155574e-04 8.642072e-05
## 4214 5626 1615 2182 5708
## 4.188291e-04 1.053900e-04 6.599395e-05 7.218745e-06 1.864302e-05
## 871 2613 6116 261 1281
## 6.018774e-06 5.763710e-04 2.062580e-04 4.545545e-04 1.333961e-05
## 2822 5846 2360 1740 7798
## 4.702024e-04 3.963990e-06 9.201596e-06 1.810053e-07 9.181341e-06
## 5930 1955 7073 6380 6962
## 9.051238e-05 5.421331e-06 3.160777e-04 5.350487e-05 2.347995e-04
## 7944 8278 8345 8183 7363
## 1.399126e-04 1.326573e-05 1.367399e-04 9.017524e-05 2.858122e-04
## 7917 5810 7879 745 2914
## 6.091750e-05 5.649541e-05 5.293719e-05 1.772382e-04 3.562801e-06
## 7655 2021 5547 2319 6318
## 1.985184e-04 1.743725e-04 7.342544e-04 1.847657e-04 4.537815e-06
## 7703 4312 7822 3484 5466
## 2.141058e-04 1.101048e-04 1.765605e-05 2.371229e-05 4.943902e-05
## 4360 6289 8101 4624 9838
## 2.263916e-05 8.727185e-06 6.519844e-04 2.998199e-07 2.966004e-04
## 4600 1126 3247 4791 4698
## 1.649558e-04 6.848531e-04 3.515173e-04 1.671883e-04 1.763276e-04
## 5440 6019 9643 688 196
## 3.183064e-04 5.696357e-04 4.058392e-07 1.190911e-04 6.800072e-04
## 835 10 2222 8454 8033
## 2.602549e-06 9.474875e-06 4.549489e-04 1.437329e-05 7.151850e-05
## 129 2966 259 7356 6714
## 9.611643e-04 1.229637e-04 1.361073e-03 3.611797e-04 8.925513e-04
## 8856 3509 9677 8171 6153
## 4.838507e-06 1.786082e-06 9.600399e-05 1.195609e-04 3.104159e-04
## 2290 3347 9228 7341 4625
## 1.226294e-04 4.362084e-04 2.128598e-04 1.126698e-04 1.349100e-04
## 5760 765 4844 9169 7967
## 1.659133e-04 2.089327e-04 1.133970e-04 2.212574e-04 3.768295e-05
## 3802 2744 8790 4449 7471
## 7.642532e-04 7.787630e-06 8.602858e-05 5.058688e-05 5.466417e-05
## 4398 1028 7658 2108 7199
## 1.998804e-06 1.648668e-04 5.286612e-05 6.375631e-04 8.478059e-04
## 4535 3636 2662 8651 1831
## 7.138561e-05 2.967141e-04 2.304741e-04 7.212686e-05 9.277668e-06
## 1322 282 4912 9405 6014
## 2.743597e-04 1.537993e-04 1.988446e-04 7.205289e-04 2.221732e-05
## 6792 8299 9298 6200 6580
## 6.008060e-04 1.119511e-04 2.880675e-04 1.952148e-04 6.787791e-06
## 8681 5984 1900 9975 4465
## 2.975090e-06 1.041320e-06 3.554975e-04 3.353888e-04 1.891193e-06
## 4127 8822 9888 8509 7593
## 2.879287e-04 5.584266e-04 1.295461e-05 1.833755e-06 6.347074e-05
## 4831 8111 3419 4984 9289
## 6.415541e-05 1.344182e-03 2.760356e-04 3.039353e-05 4.160997e-05
## 4208 3043 7886 322 4796
## 4.807359e-05 6.662042e-07 1.886021e-04 4.923598e-06 6.843825e-06
## 5775 7419 1355 3672 2703
## 5.754786e-05 4.233435e-06 2.445346e-06 2.892363e-05 8.465195e-05
## 7352 1601 6848 8910 1189
## 8.310819e-05 2.916706e-04 6.469989e-04 2.929977e-04 2.682908e-04
## 1905 7697 4928 7842 6608
## 4.861082e-08 6.768110e-06 7.405266e-08 5.879275e-04 2.261858e-04
## 8187 3089 630 5887 9721
## 1.079598e-04 1.406234e-05 7.785791e-06 1.249218e-04 1.323528e-05
## 5037 2791 4675 4648 7174
## 5.104892e-04 1.294682e-07 3.551788e-04 1.652430e-04 4.042612e-06
## 8708 5358 5844 3388 9977
## 1.126544e-04 1.030561e-04 4.320057e-04 7.822605e-05 6.181082e-05
## 8949 2013 5115 9149 108
## 3.810173e-05 5.356530e-05 1.087193e-07 9.787842e-04 2.860729e-04
## 6084 3678 5061 4557 182
## 1.345650e-05 7.396188e-04 1.682651e-04 5.421953e-05 8.568406e-04
## 5894 9665 1176 1757 6505
## 7.798996e-05 4.538395e-06 3.918567e-05 1.357339e-06 2.648922e-05
## 1967 6481 9240 8530 2103
## 5.718140e-06 3.208126e-04 2.587282e-04 9.728028e-05 5.103234e-04
## 209 1036 7580 6888 3279
## 2.215999e-05 1.640396e-05 5.183174e-04 2.151235e-05 2.397723e-04
## 9440 6355 5008 589 4147
## 3.925016e-06 3.095077e-04 2.345462e-07 3.504936e-05 7.971625e-05
## 7991 3098 6789 4652 1627
## 4.559452e-05 4.172143e-05 4.470611e-04 1.118306e-04 4.727603e-07
## 294 6625 5020 8797 2917
## 1.104376e-05 6.048937e-05 1.754992e-05 7.226316e-05 2.574583e-05
## 146 954 508 5247 6066
## 8.268692e-05 2.568714e-04 6.089350e-04 3.257060e-06 6.138374e-04
## 8639 2383 439 7217 7398
## 1.809182e-04 1.445573e-04 6.917853e-04 7.941628e-06 3.421106e-04
## 9191 8559 9476 7866 2834
## 9.535882e-05 1.546269e-04 2.992700e-05 8.082203e-05 1.374214e-05
## 3993 9907 2275 5445 9876
## 3.715079e-05 9.759723e-06 2.576091e-06 1.393370e-04 6.914712e-05
## 2517 690 364 5638 5471
## 2.305076e-05 5.514222e-06 1.118053e-05 9.886698e-05 1.206165e-04
## 8242 3934 6339 9362 9924
## 2.659180e-06 5.738618e-05 5.108437e-04 7.838005e-06 8.620548e-04
## 2523 7161 659 5907 243
## 8.342375e-06 2.174611e-08 1.106992e-04 1.840436e-04 6.943113e-04
## 913 8382 6150 8282 4908
## 6.040213e-04 1.442922e-04 1.331438e-06 1.322285e-04 1.900195e-04
## 9960 4692 4929 1492 5723
## 8.194223e-05 1.083293e-05 2.256250e-04 1.802240e-05 2.994030e-05
## 3183 8128 2341 7291 9769
## 1.999041e-04 3.561052e-04 1.721126e-04 7.619096e-04 4.686604e-05
## 7198 4125 9868 5573 1830
## 2.480290e-04 1.405173e-04 7.306508e-07 1.487828e-05 5.930222e-05
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## 2.104378e-04 4.230907e-08 2.579227e-04 2.244070e-04 5.112163e-04
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## 4392 2975 3435 4476 8164
## 1.719145e-05 7.086162e-04 6.552785e-05 1.840334e-05 1.622601e-04
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## 2396 6638 7314 5350 7841
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## 7399 1003 3647 2902 9409
## 1.731717e-05 3.314872e-06 1.292725e-06 9.544707e-05 7.572874e-05
## 5392 4941 1819 5698 7759
## 3.288915e-04 7.466405e-04 1.554948e-09 3.808487e-06 6.725391e-05
## 1122 8097 293 7716 1450
## 8.469794e-05 1.392291e-04 1.509183e-04 3.582748e-04 4.956270e-04
## 6940 1556 1670 3261 9800
## 5.123995e-04 1.092037e-03 5.994333e-06 6.542786e-06 2.041568e-04
## 2982 1352 6727 2884 6918
## 2.715300e-05 2.974041e-05 9.269891e-04 1.586822e-06 8.487051e-05
## 1489 6156 9778 2347 3778
## 5.693945e-04 4.778949e-04 4.097014e-06 1.088313e-04 2.075637e-05
## 187 461 7509 9754 7750
## 7.880047e-05 1.806566e-05 6.531282e-05 1.140600e-03 1.172685e-04
## 1004 6428 5176 2933 6699
## 2.739860e-04 2.906302e-04 3.124619e-04 4.876345e-05 4.037852e-04
## 9072 2029 8631 7105 6778
## 2.784525e-04 4.104418e-04 1.167964e-03 1.825273e-06 9.933957e-05
## 6193 2723 8650 2544 1589
## 9.976498e-05 3.238202e-04 6.315867e-04 1.709655e-04 1.382887e-04
## 9110 1132 9801 2713 8999
## 1.011061e-04 2.781937e-07 3.572484e-06 1.115435e-05 4.571430e-05
## 2308 8853 3568 7773 2934
## 5.480670e-04 1.242380e-05 4.160324e-04 4.814500e-04 1.188088e-05
## 6397 7523 5496 7980 8358
## 1.226502e-04 1.448080e-04 1.056427e-05 1.670825e-06 7.163513e-05
## 3176 2819 3331 7848 9018
## 4.259647e-04 1.532075e-04 1.500391e-03 1.649630e-04 5.064612e-05
## 3598 560 8522 485 4604
## 9.433561e-07 6.641679e-04 2.886111e-05 1.424047e-04 5.711801e-06
## 7020 8746 4956 5270 582
## 3.458246e-08 3.379003e-06 9.500696e-05 2.795817e-04 2.890446e-04
## 700 7847 403 7556 6844
## 5.104781e-05 2.310590e-04 4.429821e-04 5.430710e-04 5.272713e-04
## 8349 5712 3943 3025 6746
## 5.630547e-06 1.506760e-05 2.405444e-04 3.032388e-04 1.729877e-04
## 1046 8025 3770 9390 9589
## 2.277211e-04 1.102792e-04 1.668168e-04 1.737574e-04 9.072325e-05
## 5510 3604 7805 9697 6172
## 8.240855e-05 4.105593e-05 3.567113e-07 4.531181e-04 2.626701e-05
## 1552 624 115 5691 1474
## 1.480928e-06 1.456686e-05 2.607260e-05 2.164588e-04 1.642314e-04
## 5129 4597 6452 1981 857
## 1.500178e-06 3.111035e-05 3.787029e-05 6.628257e-05 6.039938e-04
## 8332 8068 7779 7513 1793
## 1.315961e-05 5.945626e-05 1.940332e-04 6.386532e-06 4.026739e-04
## 564 9397 4454 7994 7357
## 3.974891e-04 3.067153e-04 2.070716e-04 1.765315e-05 7.869917e-05
## 6925 9610 5538 4078 8294
## 3.738383e-04 2.352503e-04 4.500597e-05 4.792763e-05 6.999347e-05
## 2702 6682 373 7496 4343
## 6.304840e-06 1.285592e-05 7.335946e-04 1.744750e-04 1.385389e-04
## 5127 1325 2716 9903 9957
## 4.332198e-04 1.062017e-03 1.639151e-04 1.093061e-04 3.705121e-05
## 8527 592 997 323 4580
## 3.261350e-05 2.327965e-06 1.121149e-05 4.483421e-04 1.037960e-04
## 4352 5184 3512 4375 2953
## 3.002602e-04 1.110641e-06 9.323868e-05 6.007924e-05 1.897077e-05
## 8859 344 1093 433 769
## 1.291043e-06 1.010169e-04 4.361792e-04 1.482244e-06 3.414785e-04
## 6564 7849 5110 924 7342
## 1.752315e-05 1.638713e-04 1.316349e-04 4.189149e-06 4.175686e-05
## 3215 9124 481 9024 3731
## 1.620608e-05 6.401703e-05 1.551735e-04 1.857647e-04 1.761123e-04
## 6179 5551 4268 7792 8570
## 1.092189e-05 3.143620e-05 2.066668e-05 7.711052e-05 3.812164e-06
## 2448 253 8862 6175 5420
## 1.916920e-04 7.195531e-05 5.728000e-05 5.685510e-05 9.502295e-05
## 1710 6169 1105 6137 8976
## 1.777605e-04 2.397447e-04 2.983616e-05 9.145303e-04 5.084086e-05
## 9938 8322 7862 9381 8901
## 7.799376e-05 3.408340e-04 1.380949e-04 1.267601e-04 3.886261e-04
## 9091 9628 8540 6283 4916
## 1.460504e-05 5.771713e-04 7.674268e-06 3.664891e-06 5.980304e-05
## 2719 2001 4650 6224 8186
## 1.366492e-06 1.867980e-05 4.999473e-07 1.815707e-04 1.404251e-06
## 2535 5771 3956 1744 2998
## 1.671284e-04 5.852913e-05 8.717670e-05 1.506173e-05 2.643517e-04
## 3502 290 1884 9160 8071
## 5.416296e-05 4.772227e-07 1.330331e-05 5.739482e-06 2.329431e-04
## 6943 473 5525 4843 2963
## 4.742891e-05 5.534225e-04 2.662864e-04 4.564768e-06 4.386711e-05
## 1416 9557 1508 9455 4094
## 1.455854e-05 1.105314e-05 2.300804e-05 1.436794e-04 7.325086e-04
## 5549 7533 3980 2681 9900
## 7.874084e-05 9.176304e-05 5.569566e-05 2.436922e-05 6.100479e-05
## 4152 4628 8913 5600 9932
## 3.642650e-06 2.227933e-05 3.483702e-05 2.806775e-04 2.467029e-04
## 8572 2035 9424 5090 7887
## 1.206242e-04 2.999830e-06 2.512074e-04 4.032087e-04 7.613965e-04
## 6368 9062 5891 5687 9438
## 3.776549e-06 5.413943e-05 2.252238e-04 1.755190e-04 2.303620e-05
## 6948 7897 6648 3315 5495
## 8.230419e-05 1.650877e-04 3.289522e-04 5.565230e-06 1.172835e-03
## 1924 1557 4165 1066 3909
## 9.742479e-06 3.933271e-04 2.926287e-04 3.175260e-04 5.023327e-05
## 4444 3807 3666 3709 9700
## 7.076629e-07 4.478986e-07 6.408827e-06 8.412560e-05 4.104840e-05
## 855 1540 5616 7053 8086
## 1.660568e-05 1.327479e-05 1.699255e-04 3.720170e-04 3.935177e-07
## 5934 7309 1335 7411 7635
## 5.349578e-04 2.540690e-05 7.145895e-05 1.889215e-05 1.473677e-05
## 8104 6954 6043 1063 4523
## 1.545722e-04 1.595187e-06 4.026669e-04 7.656263e-04 1.530702e-04
## 8057 4134 6550 8188 412
## 9.674205e-05 2.538567e-05 1.460019e-05 1.628092e-04 1.453399e-04
## 8092 7487 9004 2284 3741
## 4.928674e-04 1.731107e-04 1.629913e-04 7.402308e-06 5.666252e-04
## 7735 8885 8380 3244 9271
## 1.064773e-05 2.659209e-05 8.265662e-05 6.856562e-05 1.447387e-07
## 2151 8154 3052 5369 2181
## 6.926170e-04 4.532641e-05 1.726489e-04 8.068952e-04 6.808276e-05
## 2729 7128 4646 4711 4533
## 8.919455e-05 4.770338e-04 9.450456e-05 1.495792e-04 1.272798e-04
## 3103 6324 3507 5779 815
## 4.302556e-04 1.637739e-04 2.090127e-04 1.020747e-06 6.394233e-06
## 6151 9657 5828 7264 3382
## 2.313456e-04 9.749003e-05 1.287609e-05 9.017039e-05 2.824761e-04
## 7480 1425 1573 7120 1197
## 4.757622e-05 3.143295e-04 2.197599e-05 5.867177e-05 1.126060e-05
## 3192 25 3916 7836 6559
## 1.637932e-04 1.020412e-04 3.237035e-05 1.565328e-04 1.442813e-04
## 7745 3759 1544 4651 5167
## 3.849003e-05 1.188052e-04 5.484359e-05 1.321194e-04 2.667649e-05
## 9450 3689 5100 2210 8291
## 3.694723e-05 8.940864e-05 1.310445e-05 4.125309e-05 1.507394e-05
## 4491 853 5035 5206 779
## 1.466496e-05 1.588014e-04 2.015614e-04 1.821563e-06 2.459414e-04
## 8391 856 110 8325 1536
## 5.098453e-05 2.221923e-05 7.864139e-05 3.022947e-06 5.743965e-05
## 7717 389 7694 7171 1326
## 3.738617e-05 5.688949e-04 2.796022e-06 5.971192e-05 3.770211e-05
## 1928 90 2406 5046 5672
## 4.936530e-04 1.216067e-04 6.675677e-04 3.578155e-04 2.051241e-04
## 5153 7981 7776 7421 3199
## 3.245723e-04 3.068707e-05 6.644540e-04 3.147906e-04 7.009637e-04
## 5409 1660 2820 3407 7417
## 1.573520e-04 3.153949e-05 1.410080e-04 3.840287e-05 1.738005e-06
## 2974 8753 4674 1748 1950
## 5.593417e-06 1.887142e-07 3.299936e-06 5.447565e-06 1.369144e-04
## 5720 451 926 2032 1913
## 1.137618e-06 5.156006e-07 2.199059e-05 4.232332e-06 6.877220e-05
## 1027 7242 7380 865 5908
## 4.944593e-05 4.273113e-05 6.707745e-04 2.252985e-04 7.159681e-05
## 2470 5893 6850 3642 8238
## 1.378447e-04 1.002026e-04 1.042186e-04 9.825044e-05 8.910896e-04
## 4327 321 5138 246 1541
## 3.340433e-05 2.477522e-04 6.072491e-04 5.968334e-04 1.882226e-04
## 4601 8281 8952 9750 5173
## 2.658687e-05 2.887969e-04 5.908461e-05 3.866128e-05 3.236757e-05
## 9908 8642 6916 1307 9121
## 5.066638e-04 1.110842e-04 1.819022e-04 1.009427e-05 4.399006e-06
## 1068 9443 9078 3762 8780
## 5.913499e-04 3.132171e-05 4.612030e-05 9.582648e-05 4.753636e-06
## 2992 6379 2459 2649 9233
## 2.074039e-04 5.002298e-04 9.549935e-04 2.195019e-04 1.345177e-04
## 7258 7058 4862 8775 1854
## 3.938613e-04 9.905414e-06 3.186263e-06 1.432946e-04 6.784978e-05
## 3171 2273 5521 9880 4264
## 1.847208e-04 4.642419e-05 1.069963e-05 2.225857e-04 9.372015e-04
## 9590 8731 7638 1180 9956
## 1.132324e-04 4.793730e-07 1.032629e-04 4.691986e-04 3.612976e-07
## 2204 7401 3501 465 1587
## 7.016210e-04 3.028236e-05 1.589075e-04 8.314182e-04 1.061908e-04
## 9600 9207 4004 487 8721
## 2.926174e-04 2.632824e-04 3.195363e-05 5.642008e-05 7.585322e-05
## 1290 2226 2490 1801 7582
## 3.528655e-04 2.631703e-05 4.348288e-04 1.174707e-06 1.384125e-04
## 1608 3289 7317 8842 889
## 2.884439e-04 2.078531e-04 1.398361e-05 4.214153e-05 4.857299e-05
## 3 3210 3626 4910 4211
## 4.132094e-04 4.533269e-05 2.912001e-06 1.505279e-04 2.418322e-04
## 2402 9774 910 739 9444
## 1.103877e-04 7.218428e-05 4.004218e-07 1.254826e-04 1.674818e-04
## 6254 6933 3944 3061 6988
## 1.951080e-04 3.623167e-05 3.931240e-04 7.821211e-05 9.011309e-06
## 2083 2892 1873 6747 9874
## 1.580885e-04 3.426544e-04 2.930348e-04 7.535775e-05 9.585899e-05
## 5142 9206 1566 5578 7660
## 6.374246e-05 4.655054e-05 3.831433e-05 6.691495e-05 6.796020e-05
## 8965 7868 4439 2794 8016
## 2.310261e-06 1.197536e-04 2.370151e-04 5.564545e-06 8.929756e-05
## 526 6038 958 3628 4009
## 1.130906e-04 3.832900e-04 9.663098e-05 4.710192e-04 7.984615e-06
## 6162 1496 9222 6438 5315
## 1.057030e-04 4.986233e-04 5.541590e-04 5.726161e-07 1.184420e-04
## 5859 8094 870 8706 6571
## 7.316430e-04 2.069258e-04 4.241495e-05 6.154785e-05 2.932206e-04
## 5450 670 310 4052 4014
## 9.053684e-05 3.597967e-05 5.850821e-05 1.536137e-04 1.043683e-05
## 227 7515 9904 5465 8757
## 1.172439e-04 8.228281e-07 9.956333e-04 4.763257e-04 4.171969e-05
## 2240 1970 4035 7213 3528
## 2.051823e-04 1.742743e-06 1.090559e-04 1.173108e-04 4.723748e-06
## 3671 7977 8469 371 981
## 2.816741e-04 7.674950e-04 1.946827e-04 2.724320e-05 2.292921e-05
## 2538 5000 7393 6049 9821
## 3.411117e-05 4.588212e-05 7.928460e-05 1.798581e-05 2.469848e-05
## 9536 1287 5535 2268 280
## 6.835285e-05 2.948832e-05 2.411703e-04 2.593591e-04 2.818835e-05
## 8992 5106 3761 2679 7791
## 5.190830e-06 1.040224e-03 4.158115e-04 2.483261e-04 1.692584e-04
## 8301 2684 93 103 3875
## 9.826044e-04 1.553389e-04 9.521365e-06 4.029866e-04 4.709765e-04
## 8560 2847 4834 1185 4886
## 1.169826e-05 8.508970e-05 2.514597e-05 1.529328e-04 3.050173e-05
## 4722 4614 2761 9448 921
## 6.058279e-06 7.481547e-04 3.302332e-05 1.094188e-08 8.360547e-05
## 7920 8543 5290 9775 3249
## 9.744567e-05 6.008050e-05 3.912681e-08 2.435928e-04 3.419172e-04
## 3197 6473 2532 7947 3878
## 3.803541e-04 1.823842e-05 1.560713e-06 6.339636e-06 1.251319e-04
## 7774 7998 2156 6418 7088
## 2.358831e-04 2.407887e-08 1.421958e-04 9.424142e-05 2.819863e-05
## 7765 8926 3513 6942 7476
## 4.962827e-04 8.071373e-04 1.978800e-04 4.763294e-04 7.702232e-04
## 1310 3695 9971 6812 4773
## 2.195337e-04 2.261589e-04 6.782711e-05 1.210635e-04 6.241843e-05
## 9236 4406 5120 9182 6951
## 2.501146e-05 6.114134e-04 1.139384e-06 1.641108e-04 1.097533e-04
## 6244 6813 8699 4282 5860
## 1.158099e-04 1.700537e-05 1.688274e-04 6.169673e-04 2.018953e-04
## 3248 9164 7115 1029 5230
## 1.544165e-07 6.228192e-04 1.143113e-06 3.129552e-04 2.446814e-04
## 8589 3830 1192 5755 7829
## 7.582608e-04 9.820441e-05 3.750915e-06 3.540414e-04 2.274323e-04
## 9106 1006 8526 484 3738
## 1.216247e-06 1.209866e-04 2.567351e-04 1.932771e-04 1.507629e-05
## 8209 6094 9376 7725 5841
## 4.799985e-04 9.669048e-04 9.164536e-05 5.805941e-05 7.152068e-04
## 8772 2877 6427 4504 3250
## 4.035018e-04 8.058311e-04 1.029394e-05 1.740713e-04 1.779305e-04
## 9415 1651 9510 9270 5911
## 6.665150e-05 1.438210e-04 4.271071e-05 4.191620e-05 8.893595e-05
## 6501 5108 2835 7511 8879
## 1.319581e-04 6.314586e-04 5.489878e-04 4.176812e-05 6.792497e-05
## 298 7831 1202 8320 7321
## 1.136176e-08 2.212715e-05 3.119758e-06 8.687180e-05 5.523123e-04
## 9461 7858 1792 8352 2595
## 2.230622e-04 1.508483e-04 3.753546e-05 5.097012e-05 3.431320e-04
## 2269 9969 3321 893 9524
## 8.870959e-04 1.500210e-04 1.773114e-04 1.492716e-04 9.481337e-07
## 6372 4747 1232 4239 2589
## 3.036636e-05 2.229920e-05 4.767218e-04 5.317782e-05 1.863406e-05
## 9886 4546 9725 8996 4484
## 2.129097e-05 2.254904e-04 1.427755e-04 6.804605e-05 1.249582e-05
## 8777 7382 1874 3682 1016
## 4.847990e-04 4.248323e-04 5.828510e-04 2.077383e-04 1.398795e-05
## 5339 1697 8935 2951 7246
## 7.609921e-05 8.722589e-05 9.383419e-05 4.309972e-04 3.374896e-04
## 9139 869 1850 3740 2109
## 1.719814e-04 1.318871e-05 9.427650e-05 2.707251e-05 3.507977e-05
## 7518 6095 7995 8821 1463
## 1.519505e-03 1.905607e-08 1.243512e-04 1.485403e-05 4.843979e-05
## 6230 6655 4940 1114 3107
## 1.189321e-05 5.070840e-05 4.818400e-04 2.531216e-04 4.951540e-07
## 8235 7452 1820 1214 1851
## 2.144835e-06 6.801873e-04 4.664297e-05 9.578650e-05 3.073406e-05
## 8146 2067 3302 5715 5171
## 2.254305e-05 5.575112e-04 1.224621e-03 2.686414e-05 1.214919e-04
## 8020 7483 3459 7809 1000
## 1.820542e-04 7.680446e-04 4.992219e-06 5.894566e-08 1.801396e-04
## 5441 7325 7642 1957 5400
## 1.724363e-04 1.996288e-04 5.000990e-05 5.445554e-05 1.491137e-04
## 1134 3623 494 355 2911
## 2.575153e-04 2.909206e-06 7.302563e-04 1.941649e-04 2.126219e-04
## 9406 327 3901 2913 9345
## 2.771696e-04 6.473959e-05 7.265792e-05 6.005330e-06 3.361537e-07
## 2944 1098 9269 4813 1242
## 3.922668e-04 2.798511e-06 4.456996e-04 3.499742e-06 5.205002e-04
## 6873 2833 3162 9467 3869
## 8.829147e-06 1.615953e-04 6.474978e-05 2.225470e-05 4.737273e-07
## 3945 4248 6708 2113 2476
## 8.368909e-05 5.793072e-05 1.229919e-04 1.116192e-03 4.337368e-04
## 3251 7687 6805 8941 4270
## 6.479471e-04 4.677728e-05 1.925873e-07 3.202007e-05 6.192047e-05
## 3798 9224 4595 655 1598
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## 4975 5693 6693 2514 1249
## 7.427503e-05 1.149422e-05 3.308229e-04 2.320302e-04 2.337153e-04
## 7286 6009 6545 297 8608
## 1.514590e-04 1.480985e-05 2.184342e-04 2.013183e-04 9.417002e-04
## 5191 7229 7757 5694 7391
## 2.858111e-04 8.761802e-05 9.881180e-05 1.010653e-05 1.041275e-04
## 362 7358 7158 3929 8340
## 2.614030e-05 4.390652e-05 3.414534e-04 5.230059e-06 4.418749e-06
## 3450 8508 5279 9100 1243
## 1.248868e-04 4.804082e-04 2.245618e-06 2.761454e-05 4.688890e-04
## 5511 4346 5796 5130 5060
## 7.757730e-07 3.023613e-04 2.071863e-04 3.337285e-04 1.221557e-04
## 8703 2038 5122 5208 7446
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## 1700 9558 8420 6293 2971
## 1.021579e-04 1.137958e-04 4.055604e-04 1.355965e-04 2.618602e-05
## 5601 5458 8841 4371 7261
## 2.335718e-06 1.925915e-04 6.310519e-06 5.662593e-07 2.481055e-04
## 3272 1337 4967 2120 7021
## 8.605918e-06 6.741249e-04 5.885390e-05 4.811426e-05 1.945845e-05
## 6176 5550 9664 2548 5480
## 2.858176e-04 6.717852e-05 3.861300e-04 3.318663e-04 7.440233e-06
## 4056 9707 8019 2097 1887
## 1.041494e-05 8.441936e-07 1.054387e-05 1.061143e-04 1.498445e-04
## 5195 7955 4501 1908 2431
## 2.883110e-04 4.530518e-06 7.607810e-04 9.776052e-04 8.738942e-04
## 4412 8329 5226 9178 5099
## 1.647504e-06 3.721496e-04 6.550389e-07 2.619095e-05 1.903549e-06
## 9165 6265 8331 4680 1439
## 2.927250e-08 1.502918e-04 1.091367e-04 3.077695e-05 1.285925e-05
## 4006 4252 4344 5097 6398
## 1.089897e-05 2.893988e-04 6.807633e-04 1.304120e-04 3.859066e-05
## 5980 2334 8696 2639 2043
## 1.446943e-06 1.268955e-04 1.897997e-04 2.043695e-04 1.030985e-04
## 3839 8980 5454 9168 8002
## 8.487399e-05 1.315302e-06 4.210832e-05 5.664381e-05 2.589263e-05
## 7527 3575 5056 8691 2760
## 6.770591e-05 1.298929e-05 5.967409e-05 2.905723e-04 1.989880e-06
## 5951 2225 1055 2855 1481
## 2.712480e-04 1.054298e-05 1.945869e-04 1.221832e-04 1.364217e-05
## 6102 1453 1139 6411 7249
## 6.220569e-04 5.955688e-04 6.067273e-06 4.009758e-05 8.406482e-07
## 7902 742 1419 2005 8472
## 6.791765e-05 2.774920e-07 2.829895e-06 1.995792e-05 7.776583e-04
## 2455 5800 8083 3673 8892
## 3.077966e-04 1.133270e-04 5.857446e-05 6.017834e-04 1.005206e-05
## 1228 2912 4100 7882 7081
## 1.643128e-04 1.327287e-04 1.363878e-04 2.337275e-05 1.785713e-05
## 4869 6709 1619 2203 1794
## 3.775176e-05 3.062400e-04 4.415013e-05 1.358405e-06 7.997318e-06
## 2137 1420 1267 8001 7667
## 1.387636e-05 1.616760e-04 2.483244e-04 1.042376e-04 1.749478e-06
## 8286 5190 3453 9306 947
## 4.444284e-04 9.393922e-04 3.066241e-05 6.643901e-04 1.112091e-03
## 8997 7397 80 7104 2248
## 2.060112e-05 3.242691e-04 2.588350e-04 7.096687e-05 8.912743e-05
## 8064 8024 1207 9709 1942
## 7.204131e-04 1.482393e-04 2.281274e-05 7.983940e-06 7.348589e-05
## 667 650 5628 2603 466
## 3.151034e-06 1.413055e-04 8.258926e-05 2.632551e-04 1.666551e-04
## 7339 5111 9283 8716 7846
## 5.569233e-05 1.623916e-04 1.986995e-04 1.792577e-04 3.973887e-06
## 4150 8975 888 5865 7889
## 2.510082e-05 4.325870e-05 2.646968e-08 6.304562e-05 5.047893e-04
## 411 1272 102 2205 3178
## 1.023957e-04 1.468386e-04 2.797776e-06 4.036979e-05 1.162409e-05
## 5531 6238 2645 5366 7865
## 3.230658e-05 3.067652e-04 1.275940e-04 1.968076e-04 8.129102e-05
## 4149 4167 1849 3894 2031
## 7.085443e-04 8.176919e-04 7.720628e-04 3.162989e-06 4.422751e-05
## 1248 380 7370 3856 887
## 9.182601e-07 3.198755e-05 3.896558e-05 2.488518e-04 6.989734e-04
## 3833 3818 3257 8428 1766
## 2.600713e-04 4.410963e-04 2.901670e-04 2.124556e-04 2.781250e-05
## 1571 9749 3652 1136 9490
## 1.415914e-04 1.047104e-04 4.525403e-05 1.330177e-04 2.511138e-05
## 3283 6125 6910 4060 8500
## 2.841625e-04 2.623928e-08 1.213452e-04 4.919783e-04 1.366839e-07
## 1386 8747 3219 5266 7502
## 7.099058e-07 2.726491e-04 1.576784e-05 1.344951e-07 3.060819e-05
## 9759 7583 1514 3937 4669
## 2.385668e-04 2.712462e-04 5.571788e-04 1.094370e-07 5.527993e-04
## 1341 1580 6695 6078 9781
## 7.904307e-04 5.907037e-04 1.080940e-06 4.606358e-05 1.389007e-05
## 4634 5502 1081 2004 7098
## 1.740928e-05 1.577280e-04 8.128368e-05 4.091964e-04 1.189104e-04
## 7632 845 7950 1037 5053
## 5.831486e-05 1.457738e-04 7.554780e-05 3.094069e-05 2.708857e-04
## 2444 7880 2350 8040 9357
## 1.548969e-04 6.196322e-06 1.880797e-07 9.389353e-05 2.239089e-05
## 6423 1221 3705 7783 4610
## 1.448379e-05 2.815477e-05 3.466421e-05 1.069834e-08 7.884836e-05
## 5249 759 9986 8264 771
## 1.065577e-09 2.043107e-06 2.163641e-04 1.017914e-04 2.108637e-04
## 1312 8402 91 4907 1991
## 1.191491e-04 1.914671e-04 6.599905e-05 2.463340e-04 5.467759e-06
## 7461 3725 1075 9642 2436
## 4.203547e-04 2.631113e-04 3.468282e-05 3.612588e-05 6.184728e-06
## 9066 7748 7996 4266 9582
## 4.420622e-05 7.070654e-08 7.373535e-04 2.493470e-05 7.011874e-05
## 2621 6958 5175 8641 1937
## 2.864465e-04 1.997352e-06 1.283651e-05 3.332772e-06 3.133595e-04
## 9500 4566 9814 7300 2468
## 2.243443e-04 2.104829e-05 6.936791e-09 7.004716e-05 3.074912e-05
## 7777 5837 5273 5312 9779
## 1.008251e-03 5.919641e-05 2.633680e-04 2.271713e-05 1.995966e-04
## 3904 9145 7751 4937 7878
## 4.440694e-06 1.337300e-03 2.541788e-04 2.377192e-05 4.053064e-05
## 5354 175 5415 2363 6308
## 3.043473e-04 2.732640e-05 3.710674e-05 8.041811e-06 1.683537e-05
## 1034 9470 2653 2540 9158
## 7.017764e-05 1.088202e-06 2.270906e-04 1.216874e-05 5.464321e-06
## 6188 72 6967 8863 1394
## 2.138169e-04 6.991743e-06 2.702345e-04 5.651419e-05 4.907495e-04
## 1808 649 4815 388 2850
## 1.891656e-05 1.167648e-04 8.242175e-04 1.606479e-05 4.425430e-06
## 1681 4113 795 7758 6174
## 3.043549e-05 4.103647e-04 1.438623e-04 4.001869e-04 2.944886e-04
## 9458 6828 7235 3788 8884
## 2.614484e-04 4.075616e-06 4.032647e-06 2.184300e-04 1.285625e-05
## 7962 238 1385 5467 7078
## 6.994618e-06 5.249194e-05 7.137332e-06 7.567674e-05 1.640927e-05
## 7453 1080 5922 3268 6391
## 1.053479e-04 4.228061e-04 7.722868e-07 5.357173e-06 2.320115e-05
## 9213 7200 3903 8734 9653
## 2.597233e-06 2.138901e-04 5.487910e-09 1.305073e-04 1.823635e-05
## 6652 5329 3540 2430 6776
## 2.057831e-05 1.616294e-04 6.777189e-05 1.230402e-06 1.393418e-04
## 6037 6117 9967 778 6759
## 1.821935e-04 1.205950e-06 4.567025e-05 1.897858e-04 2.956816e-05
## 9864 8257 7788 4635 3500
## 8.285902e-06 7.979312e-05 8.266218e-08 4.509603e-06 4.668156e-06
## 6704 8112 9248 5973 9043
## 5.110861e-04 2.511213e-04 6.301769e-07 2.277122e-06 2.435548e-04
## 5651 8878 8914 6413 4810
## 1.862281e-04 8.286436e-06 4.333537e-06 4.562952e-05 9.238634e-05
## 5051 6217 3838 5306 226
## 1.179253e-05 3.315044e-04 9.898598e-05 9.151209e-05 2.388468e-05
## 8745 8172 3567 4394 9921
## 1.586762e-08 3.123985e-05 7.924210e-05 8.152548e-06 3.354027e-05
## 9219 4787 9202 2409 8122
## 3.089825e-04 6.986987e-05 8.107284e-05 5.421203e-05 2.420515e-04
## 1308 2989 21 4057 2875
## 2.937295e-04 1.259443e-04 1.384370e-04 9.747947e-05 4.124404e-05
## 9354 2233 3179 651 9088
## 5.671308e-04 3.695095e-04 1.056073e-04 4.709763e-04 7.650437e-04
## 2365 6935 3320 8528 4893
## 1.770791e-07 3.532342e-05 3.623938e-05 3.723230e-05 1.964512e-06
## 4838 7001 6731 3209 3160
## 2.594261e-05 2.165547e-04 2.179993e-04 7.915539e-04 2.422452e-04
## 974 2651 2638 8740 948
## 5.352375e-06 6.194198e-05 2.310704e-05 6.218556e-04 7.729768e-05
## 9562 8767 8584 8774 6996
## 2.395539e-04 3.544365e-04 1.542514e-04 1.317903e-04 2.191610e-05
## 8193 4325 9716 4286 5225
## 2.635615e-05 3.419439e-04 8.508866e-05 7.267351e-05 4.989409e-04
## 7614 7256 5228 3031 2498
## 3.844903e-06 1.760359e-04 2.650727e-04 1.724567e-05 1.636180e-07
## 60 5283 5079 3780 2965
## 1.347369e-04 4.227920e-05 5.039541e-04 1.228324e-05 7.739171e-08
## 9241 4136 2192 2195 5770
## 5.520324e-04 2.434358e-04 5.449524e-05 8.733082e-05 4.123405e-04
## 8847 2533 5940 5052 9654
## 1.056127e-04 5.986304e-05 7.374790e-05 4.897189e-05 2.096876e-05
## 9176 2335 8032 9023 4260
## 4.875535e-07 2.985018e-04 3.080188e-04 1.475462e-04 2.400887e-07
## 1692 5674 1470 1755 5381
## 1.029286e-05 1.316815e-03 5.313158e-05 1.165779e-04 1.247732e-05
## 5835 8893 304 5141 2168
## 4.230686e-05 1.133155e-05 1.700347e-04 4.521192e-06 2.234087e-04
## 7303 2364 8494 8044 4077
## 7.414961e-04 6.745028e-05 7.363955e-08 2.347064e-06 1.325934e-04
## 9083 4424 5804 3472 5596
## 7.341892e-05 2.343635e-04 3.539746e-04 1.806686e-04 1.267144e-05
## 8811 6252 1745 2770 4963
## 1.984608e-05 3.337596e-04 3.317266e-04 7.733835e-05 3.512039e-04
## 4171 9822 8203 6771 8593
## 1.070263e-04 4.437132e-04 6.221559e-06 1.794661e-04 1.966309e-05
## 447 892 8782 9410 4913
## 1.166036e-05 4.519345e-04 1.680009e-04 1.204711e-04 1.372406e-04
## 158 6343 9162 3379 691
## 6.580586e-04 1.782392e-05 1.442725e-06 1.349808e-04 3.444993e-04
## 5423 4851 18 5417 2419
## 6.603737e-05 8.319729e-05 6.795435e-06 3.648313e-05 4.629371e-07
## 1861 5428 392 8323 1927
## 1.555933e-05 1.423976e-05 8.483931e-05 4.957487e-05 5.486068e-05
## 960 4298 1019 5303 4731
## 1.857795e-05 7.959094e-04 6.619561e-07 1.487558e-04 6.263582e-05
## 6183 4317 2276 3069 4877
## 1.215205e-03 5.233708e-05 7.819208e-08 5.287924e-07 2.039438e-04
## 4889 9737 3397 404 7526
## 5.915500e-06 2.968354e-05 3.070572e-05 5.326454e-06 9.468066e-05
## 903 4219 3408 8574 8713
## 4.047549e-06 8.948145e-05 1.246401e-06 5.415893e-04 1.086761e-04
## 96 1550 3147 5103 6322
## 5.379942e-05 5.019493e-05 6.287275e-05 2.863576e-07 1.437047e-04
## 2737 2148 4835 137 4949
## 6.186511e-06 4.405669e-04 1.394246e-04 5.445011e-05 1.181368e-05
## 7360 4287 4247 9135 6566
## 5.966421e-06 3.183428e-05 1.623977e-04 1.694706e-04 1.361102e-04
## 5387 2413 8568 9917 4302
## 1.850468e-04 5.843472e-04 2.058382e-07 3.480818e-04 2.114847e-06
## 8712 5773 6264 5636 6298
## 9.972705e-05 8.050027e-04 3.231601e-04 1.362367e-04 3.104823e-04
## 4308 8615 4373 9568 7493
## 6.509392e-05 6.132155e-04 4.972880e-06 2.732739e-07 3.972063e-04
## 2162 3923 9845 8037 6130
## 3.743157e-06 2.519655e-04 1.205964e-05 8.855457e-04 1.622555e-05
## 2411 3758 1186 3114 7241
## 1.703457e-05 2.133351e-06 1.840006e-04 4.651860e-04 4.572874e-07
## 3465 3369 5335 5477 1724
## 4.365584e-05 4.180318e-04 4.061839e-06 1.371081e-04 4.691617e-05
## 1886 1251 472 2860 9356
## 3.092238e-05 6.336793e-05 2.564995e-05 3.308570e-04 1.573865e-06
## 4273 228 3941 849 3884
## 1.808724e-04 9.019594e-05 2.857069e-04 3.799935e-04 9.824299e-05
## 2157 3187 1047 8436 7605
## 9.905132e-05 6.977701e-05 7.942286e-05 1.631432e-04 2.170009e-05
## 5222 1491 942 3840 580
## 3.724327e-08 8.728835e-04 9.264317e-06 1.609288e-06 3.963619e-04
## 4177 334 7812 1796 7424
## 4.665584e-05 3.944196e-04 2.371059e-04 8.287166e-05 1.072603e-05
## 7293 8812 7197 4063 1959
## 5.114016e-04 2.371110e-04 9.086132e-05 1.972363e-06 1.681599e-05
## 1772 7353 5377 4932 7732
## 2.953472e-04 1.477351e-04 3.155618e-05 1.370461e-07 9.703611e-05
## 1652 9120 6425 5260 7867
## 8.105592e-05 4.505874e-06 8.723414e-05 8.754948e-04 3.990644e-04
## 6836 4319 5640 4516 1212
## 7.016244e-05 1.902173e-04 6.171883e-05 1.888886e-04 4.037723e-06
## 4653 4958 7010 9698 5164
## 1.970440e-05 3.383917e-05 1.149235e-04 1.509388e-04 1.643087e-06
## 5401 7160 1172 5605 4209
## 1.143665e-04 8.819017e-05 1.401896e-03 1.181727e-05 6.673170e-06
## 1875 7436 271 6028 9571
## 5.516483e-05 7.174918e-07 1.049569e-05 2.809010e-04 1.507354e-04
## 5359 5834 3659 5398 5069
## 1.279623e-03 6.118713e-05 6.653832e-05 5.627932e-05 1.212944e-04
## 714 8785 1233 4361 1837
## 3.275717e-07 9.559561e-05 2.809572e-04 9.405671e-05 2.439998e-04
## 6620 4388 8931 6599 1693
## 3.421372e-04 4.664029e-04 2.091909e-04 3.586773e-06 1.910138e-05
## 3074 3927 7034 1817 4462
## 1.323531e-06 4.393156e-05 1.706956e-05 1.914367e-05 2.241360e-05
## 8698 6782 7460 3782 315
## 1.050218e-04 8.761554e-04 3.537135e-05 1.372697e-04 1.133550e-04
## 8169
## 3.843330e-05Test
if (algo.forward == TRUE){
test.model(model.forward2, data.test, "Forward Selection (2)")
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 110.5 120.7 124.1 124.0 127.5 144.3
## [1] "Forward Selection (2) Test MSE: 98.2068928588799"
Backward Elimination
Train
if (algo.backward == TRUE){
# Takes too much time
t1 = Sys.time()
model.backward = step(model.full, data = data.train, direction="backward", trace = 0)
print(summary(model.backward))
saveRDS(model.forward,file = "model_backward.rds")
t2 = Sys.time()
print (paste("Time taken for Backward Elimination: ",t2-t1, sep = ""))
plot.diagnostics(model.backward, data.train)
}Test
if (algo.backward == TRUE){
test.model(model.backard, data.test, "Backward Elimination")
}Stepwise Selection
Train
if (algo.stepwise == TRUE){
t1 = Sys.time()
model.stepwise = step(model.null, scope=list(upper=model.full), data = data.train, direction="both", trace = 0)
print(summary(model.stepwise))
saveRDS(model.forward,file = "model_stepwise.rds")
t2 = Sys.time()
print (paste("Time taken for Stepwise Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.stepwise, data.train)
}Test
if (algo.stepwise == TRUE){
test.model(model.stepwise, data.test, "Stepwise Selection")
}LASSO Selection
LASSO (w/ full train)
if(algo.LASSO == TRUE){
# Formatting data for GLM net
# you can use model.matrix as well -- model.matrix creates a design (or model) matrix,
# e.g., by expanding factors to a set of dummy variables (depending on the contrasts)
# and expanding interactions similarly.
x = as.matrix(data.train[,feature.names])
y = data.train[,label.names]
xtest = as.matrix(data.test[,feature.names])
ytest = data.test[,label.names]
grid=10^seq(10,-2, length =100)
model.LASSO=glmnet(x,y,alpha=1, lambda =grid)
cv.out=cv.glmnet(x,y,alpha=1) # alpha=1 performs LASSO
plot(cv.out)
bestlambda<-cv.out$lambda.min # Optimal penalty parameter. You can make this call visually.
lasso.pred=predict (model.LASSO ,s=bestlambda ,newx=xtest)
testMSE_LASSO = mean((ytest-lasso.pred)^2)
print (paste("LASSO Test RMSE: ",testMSE_LASSO, sep=""))
print(coef(model.LASSO,s=bestlambda))
plot(ytest,lasso.pred)
}LASSO (w/ filtered train)
if(algo.LASSO == TRUE){
# Formatting data for GLM net
# you can use model.matrix as well -- model.matrix creates a design (or model) matrix,
# e.g., by expanding factors to a set of dummy variables (depending on the contrasts)
# and expanding interactions similarly.
x = as.matrix(data.train2[,feature.names])
y = data.train2[,label.names]
xtest = as.matrix(data.test[,feature.names])
ytest = data.test[,label.names]
grid=10^seq(10,-2, length =100)
model.LASSO=glmnet(x,y,alpha=1, lambda =grid)
cv.out=cv.glmnet(x,y,alpha=1) # alpha=1 performs LASSO
plot(cv.out)
bestlambda<-cv.out$lambda.min # Optimal penalty parameter. You can make this call visually.
lasso.pred=predict (model.LASSO ,s=bestlambda ,newx=xtest)
testMSE_LASSO = mean((ytest-lasso.pred)^2)
print (paste("LASSO Test RMSE: ",testMSE_LASSO, sep=""))
print(coef(model.LASSO,s=bestlambda))
plot(ytest,lasso.pred)
}LASSO calls
Peforming a lasos call is pretty straight forward. GLM-NET peforms 10-fold CV to determine an optimal penalty parameter.
The coefficients are easy to extract and making predictions are straight forward. It is possible to make ASE style plots like we did previously but it takes a little extra programming. See me if interested.
# summary(model.forward)
# summary(model.stepwise)